You don't need a sleeper between NY & Wash, it's a 3- to 4-hour day trip, depending on whether you choose the premium Acela service or a regular train. That's called the Northeast Corridor, which is Amtrak's busiest line, and trains running about once an hour during the day. Of course, if you really want private rooms, you could book it on one of the long distance trains, but you'll be paying quite a premium.
Between Wash & FL, Amtrak runs single-level Viewliner sleepers. There are Roomettes and Bedrooms, both of which sleep 2 adults on upper & lower berths.
Roomettes are the economy sleepers. The older cars have toilets in the Roomettes; the newer ones do not. There is no private bathroom; the toilet (when there is one) is right next to the lower berth, with a fold-down shelf-like cover. All Roomettes have sinks. The Roomettes are half the car width, and there is no space to move around in night mode. In day mode, there are 2 opposing seats. (The sleeping car attendant will convert your rooms between day mode and night mode.)
Bedrooms are more spacious. Each bedroom has a private bathroom with a toilet and shower; a sink is in the room. They occupy the full car width, so there is more room to move about in night mode. In day mode, they have a sofa and an armchair. During the day, it might be possible for all 4 of you to squeeze into one bedroom, with 3 on the couch and one in the chair.
All sleeping car passengers get the same food service, which right now is not so great, consisting of pre-prepared reheated meals. All meals and non-alcoholic beverages are included in sleeper fare. There is also a cafe car where you can purchase snacks and a few light meal options.
There are only 2 bedrooms per car, so you'll want to book as soon as possible if you want bedrooms. If you want 2 roomettes, you can request 2 that are directly across the hall from each other, but only by phone, not online. Another option is to book one bedroom and one Roomette in the same car; everyone could gather in the bedroom during the day and have access to the bathroom, and then 2 could use the Roomette for sleeping.
Amtrak does not have open berths, or couchettes like European and Asian overnight trains. Passengers who don't want to pay for a private room sleep in coach. Amtrak coach seats have an exceptional amount of legroom. They recline quite a bit, but not to "lie flat". Coach passengers currently do not have access to the diner, so they either purchase all food from the cafe car or bring their own onboard. Amtrak does not have any restrictions on bringing on food, but there are no preparation facilities. Coach seats are not preassigned, and it may not always be possible to find a pair together, let alone 4 together.
During normal times, there are 2 daily trains between NY and FL, stopping in Wash. They have identical equipment. The only difference is that the Silver Star takes a more inland route than the Silver Meteor, so it's a longer trip.