So, are bigger motherboards better, or do the just have more expansion slots?
Should I consider a larger case to start with?
They have more expansion slots and more "relaxed" specs with regard to CPU coolers, RAM etc. You can fit components easier and get a better airflow also.
A case to house a ATX board can be had for cheap nowadays and will be more serviceable in the long run.
If you use Windows, don't forget that it will need to be activated for the new system; replacing the mobo means a new PC as far as the OS is concerned.