Is JGame the ticket? Should I consider something else?
Personally I'd recommend Slick2D
, its probably the best and well supported 2d java games library, its powered by opengl as well as having accelerated sound (openal). A good community around it and some nice tools for various things (fonts, particles, tmx map editor support, xm/ogg support, etc).
How much extra work do I end up with if, say, I just use Java and interface directly with openGL or something?
Going directly with OpenGL is a lot more work, since you'll spend a lot of time writing boilerplate code and fiddling with stuff like texture loading, etc. If you just want a game up and running quickly better to use a library or engine.
One last question, possibly an odd one to be asking on a board called JavaGaming.org, is Java a bad choice? Is there any reason why I shouldn't be using it, and if so what language would make my life easier?
I'd say the language you use doesn't really matter much, if you enjoy working with it, it should be fine. People will seldom care what language its written in and more what the game is like. There are some domains though where it would be advantages to use other languages for example, Flash if your aiming for web portals or want embedded ads. Java is a pretty good choice these days as its fast, portable and has probably the best tools (IDE's, Docs, Build tools, etc). Higher level languages like Scala, Ruby and Python might help you save time and be faster at prototyping but do have their disadvantages too.