In coach, you can certainly access the diner, but meals are not included in the fare. When you leave your seat, I'd recommend you take anything really valuable with you to the diner. (Overnight kit, reading material, etc. can usually be left in your seat or perhaps stuffed into your main piece of onboard luggage.)
I haven't ridden the Meteor, but I've ridden the Silver Star, Tampa to Baltimore, which runs in a lot of the same route in Virginia and Florida. Great scenery. Middle of coach is best if you can find a seat there. Standard electrical sockets at seats, so you can plug in laptop, DVD player, recharger, etc.
I've written a couple of articles with tips that may be helpful for overnight Amtrak travel, including coach:
• Planning a Trip on Amtrak? Tips for Getting Yourself in the Right Frame of Mind
• Riding an Amtrak Train Overnight — Tips for First-Time Rail Travelers
The second one (Riding an Amtrak Train Overnight) includes a number of very practical tips for a coach trip — things to take with you, what to expect, how to prepare, etc. Like a light blanket, change of clothing, etc.
Hope it goes well — LH