My first real "big" trip was to K'ton by Amtrak (from Washington DC), transferred in NYC to Rutland VT.
There is luggage allowance: 2 bags carry on and cannot check bags (per the ticket I purchased that time). I brought 3 pieces carry on: 1) ski bag, 2) small suitcase, 3) large shoulder bag.
But no one bothered to check I had 3 bags. I asked before I boarded the train and was told it'd be fine.
As for storage,
@NYC2VT is correct, there are larger luggage storage areas at the end of each cart. So you can opt to sit somewhere near the storage area to keep eyes on your suitcases. The space was big (& wide) enough that I was able to lay my ski bag flat on ground.
There are overhead compartment for storage but my ski bag was too heavy for me to lift and put it up there.
There are "steps" as you get on and off the train. Amtrak staff helped me w/ my ski bag, since it was quite "long". Don't hesitate to ask for help if you need. It can be tricky to maneuver w/ the ski bag as you get on and off the train.
The train i took was the 2pm'ish train out of NYC Penn station and arrived to Rutland around 8:30 pm. It was not an "express" train. I know there are express trains out of NYC on weekends to accommodate weekend skiers to VT.
Yes there is a public bus from Rutland to K'ton. Many K'ton staff take that bus to and from work. May get crowded in the morning bus (~7:30 am). But if you get on at the terminal station, you will be able to find seat for sure.
There are several hotels along that bus route in Rutland.
There is a Walmart (practically) next to Amtrak train station.
Hope my answer helped.