You can find the title and registration costs on each states dmv website.
Regarding where you register it, don't worry. Register it in whatever state you wish or whatever state you happen to be in if it is advantageous as in cheap reg cost.
You DO NOT need to be a state resident to register a vehicle.
I've moved 9 times in the last 18 years and I re register vehicles sometimes right away if I'm being reimbursed for the cost as part of my moving package or not until they expire otherwise. I have bought vehicles in states where I was living but not a resident and just titled and reg there. No problem.
Same with your drivers license. Don't worry about it. You have a good excuse for your state dl if you get pulled over. What are you going to do get 5 licenses a year if you move that much? I've only been questioned about that by the cops maybe once or twice ever...... And been pulled over a few more times than that! Hahaha
Even if your dl does not match your plates. It's not a big deal.
I currently have valid drivers licenses in 3 states and vehicles and toys registered in 3 states.
No way I'm going to mess around with changing everything over every time I am in a different state.
Don't sweat the little stuff.
Some other advice. If you travel, some warranty on a used MH will probably be tough or impossible to collect on if you are not where you bought it. Also a new engine unless it is really high miles typically means the prev owners beat on the vehicle or didn't maintain it. Stay away from that one.
Look in the southwest this time of year. Tons of RVs for sale by snowbirds that made their last road trip. Lots of deals to be had.
Not sure what type of MH you are looking at or want, but try to find something on a popular chassis so it's easy to get repairs anywhere. IE. Chevy Ford, cummins, etc.
Hope this helps.