How to socialize a big dog with two small dogs?

So about a week ago, I found a medium sized puppy like dog wandering the street so I decided to take him in. He was at a shelter for the majority of the week so in total I've only had him for about 24 hours. Come to find out they identified him as part lab part pit bull, which still has me a little bit on edge even though he's been nothing but sweet and loving with me the entire time I've been with him.

We're not entirely sure if we're keeping him because the thought of someone adopting him is still an option since we already have a house full of pets but for the time being, we're trying to figure out how to socialize him with our two small dogs that way we don't have to keep him closed off in an area of the house.

One of our dogs is a bichon frise. He's super playful and friendly and all around a bubbly dog. Our other dog (who was actually lost and found several years ago also) is a mystery. We like to think of her as maybe part chiwawa because she is very fearful and a little snappy at times so I'm more worried about how she'll interact with this dog we found over our bichon since he's more outgoing with innocent intentions.

What are some things I can do to slowly but surely get them comfortable with each other? He's been closed off but with one of those baby gates and so far they've been sniffing each other quite a bit and are acquainted in that way but they haven't had much physical interaction without that baby gate in the way. Since this dog is still very much a puppy but bigger, I just don't want to see any of the three dogs get hurt even during innocent playing.

By the way, just to give you all a visual the dog I found is 40 pounds. Our bichon is a little more on the smaller side at about 10-13 pounds and even though we think our female dog is part chiwawa, she's a little bit bigger than our bichon at about 15 pounds.