A cheap $500 generator isn't going to fully power most houses
I got a 7.6kW generator for $550. It's just open frame and loud AF. If you have gas heating appliances it's more than adequate, if not then it isn't.
You'll also need a generator interlock installed if you want it to actually power the house instead of running extension cords to a few appliances.
To do a legal permanent install, yeah. But you physically could turn off the main breaker, connect a generator to a branch circuit (perhaps on a sub-panel) and run the important things in the house that way. Lock out the main breaker (with an actual lock, preferably) and turn off any unneeded circuits for safety. Use a breaker at the inlet panel sized for the branch circuit wiring. I have nothing like this connected, but I do know for a fact that it's a viable strategy if you don't get carried away with what you try to run.