Try google "how to toddler proof your home" and you'll get plenty of articles to help you out. 

But it's not you who should be purchasing items for the child in your home. That's on the father to pay for. He'll need perhaps some guidance so he doesn't go crazy shopping. Remember the kiddo is only going to be there 48hrs  twice a month or so. 

If you'd like to get something for just you and the child to share together, think about books. Reading to the little one can be a bonding time and quite enjoyable. You can probably just check out the toddler dept. in your local area rather than purchasing and rotate the books. 

I'm surprised there is not to be a 'trial period' where he slowly has the child a bit longer over time. If she has never spent the night anywhere other than at Mom's or been away from Mom, she could very well put you and your BF through a rough spell at bedtime for a while. Especially if she has been co-sleeping with Mom. 

If he is to supply weekend clothing instead of the mother sending a packed bag, Dad will need the basics. Socks, underwear, pjs, a few outfits. And remember kids grow fast. Don't over buy. 

Meals could also be a hassle depending on what type of eating habits Mom has set the routine for in her home. Some of these tots never eat anything but chicken nuggets and would rather die than try a green bean. Being the father knows very little about his daughter and has barely spent time with her that you and BF are going to be pretty frustrated with your sudden new little visitor. Dad is all but a stranger to her and you are a stranger. This isn't going to be easy. Be sure Dad is aware of any allergies and knows any medical history. 

What you don't want to start out with though, is you being the main caretaker. This man wanted this child, wanted to be an involved parent and you need to insist he do the bulk of the caretaking. 

Toddlers are adorable but also MONSTERS. Don't take anything personally. They are at the age where they are totally self-centred and have no clue about anyone else, yet they're starting to be able to converse properly. They are starting to understand the boundaries between themselves and the world, their own power and lack of power. They test everything. 

On the other hand so much is new to them and it's amazing seeing their wonder at the world. 

Toddlers shouldn't be sticking fingers in electrical sockets at this age, but basically medication, alcohol and possibly cleaning supplies should be out of reach. 

As @twoviewpoints said - the main thing is making sure you are not this child's main caregiver. Some men are dolts like that. His kid, his problem. I do take care of my stepkids, but we both have kids around the same age, so it's more swapsies. 

That has value to you.  Glass thing that are low and can get at.  Sleep well the night before 

Is this child just turned 3, almost 4, or somewhere in the middle?  That might dictate what you need to do.  That said, I have had my SO's 3 year old living in my house 50% of the time for over a year, and she was visiting regularly prior to that, and I have not done much toddler proofing.  She doesn't stick her fingers into electrical sockets, put things into her mouth or get into the cabinets.  She's good on stairs and hasn't had a toileting accident since she was about 2-1/2.  All I've done is put cleaning products, medicines and knives out of her reach, and put away the few fragile decorations I had for the time being.

A 3 year old will need clothes, toys and books.  For EOWE, she won't need much in the way of clothes, but she will need some.  Even if her mom packs her a bag, unexpected weather changes might mean she needs items that weren't packed.  The first winter we foolishly thought that SO's kids would be fine with just one winter coat each that went back and forth between mom's house and dad's house.  That worked well until they came from school/daycare on a warm Friday having not worn their coats, and it was below freezing by Saturday morning - now they have just about everything at both houses.  You might want to have some first-aid supplies for a child - children's tylenol, motrin, benadryl, character bandaids, etc.  She'll need a toothbrush, kids' shampoo, maybe detangler.  It'll be OK if you don't have absolutely everything you need the moment she arrives - you'll figure out things you need as you go along, and she might like to help pick out toys, things for her room, clothes, etc.  One thing you will need immediately, if your SO doesn't already have one, is a carseat.  If both of you will be transporting her, it might be easier to have one for each car.  It only took having to move carseats from my SO's car to mine once or twice before I ran out and bought my own carseats.  They are a PITA to move.

I would also stock up on some kid-friendly foods and snacks.  I hope the BM will be cooperative enough to let your SO know the child's routines, likes and dislikes - that will make the transition easier.  

I agree with the prior posters who recommended letting your SO do the heavy lifting where parenting is concerned.  This is *his* child, and if he fought for her, he should be the one caring for her.  

Good luck.  I can tell you that my SO's 3 year old is a total joy 80% of the time; I hope you'll have a wonderful time with your SO's daughter. 

Getting a "blank space" ready. Basic bed with white sheets, bookshelf, generic toy box, dresser. Dont buy anything else before SD comes. Shes just about at the age that she has an opinion. Take her to Target or whever and let her pick out a few things. Socks, underwear, jammies, 2 or 3 mix and match outfits, cute sheets, hair care supplies, bath stuff, maybe a cutesy piece of art for the wall. Then let her and daddy unpack it and put it all away. She can help in the creation of her "nest" and its also  good way to give her a hands on lesson in helping around the house. "Whoops, SD, thats not where the wrapper goes! Trash goes in the bin. Good job!". Then, over the next several visits, fill in empty spots. Let her pick a toy or a game or a book every weekend until she has a good stockpile. After that take trips to the library or the museum. If she asks for more stuff, direct her to the stuff she already has and your DH can play a game or read a book with her or walk to the park or have her help make lunch. Anything.

As far as toddler proofing..i probably wouldnt bother beyond making sure her bed is toddler safe and theres a lock on the dangerous chemicals cabinet. And hide your cosmetics. 

Remember, this is time shes spending with her dad. Maybe you can use it to have some "you time" if you want?

When my kids were in the toddling stage I had plastic cafeteria plates, plastic cups, hard plastic silverware, basically anything they dropped or threw on the ground would be break and spill proof. Anything possibly dangerous below the level they could reach was locked up. Nothing was white, everything was neutral with some kind of pattern that hid stains, dirt, paint, etc. 

My days went like this: feed, wear them out, naptime, repeat.  Make sure dad does the heavy lifting of parenting when he has HIS kid. So many single dads look for a replacement caregiver who will do everything the mother did so they can carry on as they did before. 

It's your own mental/emotional/physical health, as well as your relationship with your SO.  

While you have lots of good practical advice here about what to get and how to prepare the house for SD, I think the more important question (for you and your SO) is how to deal with THIS:

"I’ve only met her once because the BM wouldn’t allow it. My SO only saw his daughter without me,"

Sounds like you have a BM problem already and it's something your SO need to address and tackle NOW!   It doesn't matter how many cute toys, clothes, and household items are bought, if it turns out this little girl is being coached by BM to dislike going to her father's house then you and your SO will have challenges with this child and of course, with the BM interfering.  You may have many bigger problems ahead of you.

Sit your SO down and tell him he needs to read up about "parental alienation."  Understand what the tactics are and how to recognize symptoms of it.   The fact that BM made it difficult for him to see his daughter and he had to fight for visitation is already a sign of a problem.  

Oh, and as far as practical advice I would add one item to your list:  Waterproof mattress pad/cover.   You may have many wet nights ahead!

Here's a big one for living with a toddler - hide all of your nice shit lol 

Coffee table books? forget em. Decorative objects on a console table? nope. Fancy shampoo and conditioner in the bathroom? not unless you want em used to make 'potions' 

Seriously, toddlers get into everything. It drove me nuts when SD was a toddler and did it, and it's driving me nuts now that BS is 13 months old and starting to do it. Keep your decor pretty minimal and keep your expensive bathroom products out of reach until they're a bit older and you can start teaching mine vs. yours. My SD is getting pretty good now about not touching other people's things. She started understanding it around 4-5 and we've really pushed it. 

If she picked up something decorative, we'd say "SD that's not yours. You have toys to play with, don't play with our things." and now at 6 we never have to give reminders. Because of this, she's both of our family's favourite kid to have over :-) 

My SK as a toddler was pretty well behaved-- but in addition to all the advice you've received already (which is spot on), I'd say make time for yourself and your SO. Toddlers have a way of coming into the space and taking over, especially if dad really HASN'T had to do heavy parenting up until now-- it will be easy for him to go easy on her and let little things slide and turn into a disney dad. Talk to him now about agreed upon rules and boundaries-- so that way you're both on the same page and you're not as likely to be back here in 6 months time upset that a 3/4 year old and her disney dad have taken over your home EOWE and it's misery!

Cover the electrical outlets and watch what she sticks up her nose.  But maybe the sticking things up their nose is a boy thing.

You may also want to put toddler clips on your cabinets and drawers.

My mother taught SS the joys of pot and utensil banging when when he was a toddler.  He enjoyed it so much that we just gave up.  Fortuantely he grew out of  it.  Unfortunately my 73yo mother hasn't.  She is fond of waking us up when we are visiting by banging pots at our bedroom door.   Yes, my mother can be evil.  And she enjoys it.

Except when my mother would visit and get hold of him SS was a joy as a toddler.  He was mellow, happy and extremely easy going. So much so that we would fairly frequently be asked if there was something wrong with him.  Nope, he was just a very mellow and well behaved toddler.  We had a couple of incidents of him trying to stick things into electrical sockets (we bought covers) and putting things up his nose (two trips to the Pediatrician to get pebbles or small game pieces removed) but other than that... he was a gem.

Don't get me started on his teens though.  Ughhhhhh!

I have no bio children and have found it useful for my sanity to pretend as if the skid does not exist unless the skid is in my house. I do not want my relationship with dh to be skid-centric and neither does he, so we do not speak of the skid unless she is in our house. It has helped us separate our relationship time from skid time. I also have dh put sd9 to bed an hour before we go to bed so we have our alone time to reconnect as a couple. Your relationship with your SO is the most important.