What should I do next?

Hello everyone, my wife and I have a feral cat we've been feeding for about 9 months now. Intact male, at least a few years old. He's very cute and I had an outdoor tuxedo cat (lived to 16) as a kid that looked very similar to this cat. He's a local cat, I have seen him sporadically at our house for the past few years. He gets fed by me and some of our neighbors - we live out in the country. I think he lives in a local farmers barn the majority of the time where it's warm. When he first came to us (9 months ago) his paw was injured and he had a big gash on his back, those have both healed nicely. His coat is also much shinier now. We live in Canada and so now that it's colder and with snow on the ground we don't see him as much but I fed him today and he came inside.

We would really like to trap him, neuter him, and keep him, mostly indoors.

So far, we can pet him if we give him milk - he really likes milk. He occasionally hisses at us not but not often, and never swats or bites. He's pretty skiddish with sudden movements and will back away. We have a walk out basement and so we've left the door open and he's toured around our basement then gone back outside (1 time he loafed under our bed). We closed the door once on him and he got anxious and was trying to get out after he was done eating. In the summer he likes to laze about, from a safe distance.

Obviously neutering him is next up on the list but after that I'm not sure. We don't exactly have a room we can dedicate to him once he's inside so he can get comfortable and what not so I'd like your opinions on alternatives or if it's even a good idea to trap him and "domesticate" him to begin with. Last pic is from 3 weeks ago. I've been reading alot on the subreddit and have already gained a lot of information, thanks!