Holy crap dude or dudette, slow down...
You will need outerwear, snow pants, jacket, gloves, goggle, hat/helmet. Your Spyder jacket should work fine for learning. Hopefully you got some ski/board pants you can use. Definitely have a pair of goggles.
You can rent snowboard boots with the board.
Driving conditions are going to based on the weather. Since you are talking New York, I would expect that you have driven in the snow and ice before. Same rules apply.
If you have the gear that I listed above, $300 should get you there and back without much of a problem. Just don't spend it all at the bar...