I lived in Tahoe for many many years. I prefer North Shore to South Shore due to the vibe. Getting to the North from the South on TART is a huge pain in the butt. Car rental would be key (although I am not sure about the age limit).
Squaw was my absolute favorite place to ski (but that could be because that is where I had my pass). Alpine was great, even Homewood was fun on powder days. Flatstar sucked (IMO).
Don't worry about the weather/snow. The big dumps usually come in late December/early January.
If you manage the car rental or are willing to take the trek on TART.....DO IT!! It is so worth it.