Car -- no problem. Chains -- seriously?
Gear -- Ski jacket is fine; some kind of waterproof/breathable pants are advisable. You do not want to wear jeans. Similarly waterproof/breathable gloves are a good idea. Goggles (get 'em basic orange) are a good idea but not an absolute requirement. When you rent your board they will rent you the boots. You cannot use street shoes on a snowboard.
Hunter used to have a beginner package (rentals, lower mountain lift ticket and lesson) for $79. Can't imagine where you'd blow more than another $200.