RE: Choice of lake - Will you have your own means of transportation or will you rely on public transport? Would you prefer to stay somewhere very developed or as serene and undeveloped as possible? Or something in the middle?
(Kawaguchi has all the fun of the fair - Motosu is the least developed).
RE: Choice of accommodation - Would a minshuku suit you? Or are you looking for something with a higher level of service?
RE: Alternatives - Are you dead set on Fuji? Did you also consider Yatsugatake area?