im not sure what the correlation between a freewheel and the rims quality is but either way....
it depends... on average most people run gear ratios like
and so on.... if you are looking to run something like those you will need to have a cassette backwheel. if you are running a freewheel in the back then you will need to get a cassette hub to be able to run any of those sizes. If you already have one of t hose sizes then you may be able to just get a new driver or cog to go smaller. Also you wouldnt necessarily need a whole new wheel, you could keep the same rim and have a different hub laced to it, but depending on what rim you have it may be better in the long run to just go ahead and buy a whole new wheel.