It sounds like you'll be on two trains for this trip - a Northeast Regional from Providence to Penn Station in New York and then either the Silver Star or Silver Meteor from New York to Orlando.
Service on the Northeast Regional tends to be a bit more sparse- think of it as a connecting flight. There's no baggage car, so you'll have to have your luggage with you in the coach car. Each coach seat has power outlets so you can operate your laptop or other personal electronic devices for the trip. There may also be a business class car - you can upgrade to Business class for a small fee and that gives you access to a complementary beverage, a newspaper, as well as slightly more legroom. The Northeast Regionals have a Cafe Car that serve snacks, beverages, and light meals like hot dogs, sandwiches, etc.
The long-distance trains on your route (either Silver Star or Silver Meteor) have slightly different service - no Business Class, but there are Sleepers available, although those tend to be quite a bit more expensive than regular coach accomodations. The sleepers would be a Viewliner car built in either 1987, 1988, or 1996 and your room in the sleeper would be either a Roomette or a full Bedroom. Roomettes comfortably can hold 1-2 people and have an in-room toilet but no shower. Bedrooms have a complete private bath including shower. Additionally all sleeper passengers get full attendant service (turndown, make up bed, coffee, and newspaper), meals included in your rail fare, in-room climate control, in-room power outlets, reading lamps, etc.
Should you choose to stick with coach, it's pretty much the same as coach on the Northeast Regional. The major difference is that the train will have a baggage car, allowing you to check baggage, as well as a Dining Car in addition to the Cafe Car. The Dining Car allows you to have full meals (breakfast, lunch, and dinner), is reasonably priced, and is pretty good.
In general I'd advise bringing a few books or magazines or personal electronic devices to keep you entertained for the trip, especially the New York-Orlando leg. If you're travelling in coach, a blanket, eyeshade, and ear plugs may not be a bad idea either. Bring cash or plastic so you can eat in the Dining Car or Cafe Car. Also if you travel in Coach, you might want to bring some personal wipes and deoderant or other toiletries with you so that you can freshen up - there are no shower facilities available for people in Coach, so those personal wipes can be a lifesaver. Each coach car has its own bathroom so you can wipe down there.
Overall: pros - taking a train is a fantastic way to see the scenery as you travel and meet new people. Security's not a hassle, you can get up and walk around and legroom is better over an airplane so you don't feel cramped. Dining Car meals are as good or better than you average roadside fare and certainly better than what you get on the airlines these days.
Cons - It can be a long trip (the NYC-Orlando leg alone is nearly 24 hrs from departure to arrival) and if you're travelling coach, you'll not have some of the creature comforts you may always want (like a shower close at hand!). Also if you're travelling alone in coach, your seat mate will probably be someone you don't know - don't think of that necessarily as a con, but an opportunity to get to know someone. Also, in regards to what the poster below says, Amtrak can often be late outside of the Northeast Corridor - that's not the fault of Amtrak, but the fault of the freight railroads who own the tracks. Because they own the tracks and control the dispatching on those tracks they'll give the right of way to their freight trains rather than Amtrak's passenger trains. If you want to do something about it, don't avoid Amtrak, instead complain to your Congressman and ask for more funding for Amtrak so they can build their own trackage and not rely on the freight railroads as much or so that passenger trains get the right of way.