Great answer from Steven. Basic, short answer about the difference is size. Civic is smaller, more fuel-efficient than the larger, family-oriented Accord.
I drive a 2005 Civic Hybrid with manual transmission. While it looks boring (and the body is plain and run-of-the-mill silver), I love it. I average 45 miles to the gallon, both city and highway. It is very comparable to the highly-touted, but much more expensive Prius, by the way.
I would definitely recommend you get a Civic. I think that you will find it cheaper anyway than an Accord. Your first car should be a coupe (2-door, unless you buy the hybrid which only comes in sedan), and I personally think a stick.
The model year is not as important as mileage, number of previous owners and maintenance history. Well-maintained Hondas will last forever and ever and ever. I suggest you search private party listings and try to avoid the car dealers.