Regulations on this will differ by state. The best move would be to find a local real estate lawyer. They wil instruct you on how to file all the proper paperwork with the local government, and also advise you on things you haven't thought about, like how to structure your wills to make sure everyone is protected in the event something unfortunate happens to either of you.
Also don't use this private transaction as an excuse to save money to skip any steps. Go get the title search and inspection done. You don't want any surprises. If the inspection finds a fundamental problem, you might still go through with the purchase, but at least you'll know up front what you're in for.
That's good advice, thanks! I'm in Texas specifically, but you're right contacting a professional is the right way to go. I guess I'm just thinking about what the process in a general sense might look like.
As for wills: Her will is set up to leave property to me, and finances to my brother. My will leaves everything to my wife, then to my mom, then brother. But if the house deed is in my name, does this matter?
As for home inspection and related: I'm seeing this as an opportunity to get a more detailed inspection than usual. I've found someone who is a bit expensive but is very thorough, using things like flir cameras to inspect water pipes and such. And I've been disregarding any realtors who say inspections aren't necessary.