Hi Bassmount, Welcome! I'm new at this, as well. We started a couple weeks ago. I'm close to your neck of the woods, in Winston-Salem. I don't have any info regarding how different GPSr's work in this particular area, but I bought the Garmin Legend (the blue one). It wasn't the low end and wasn't the most expensive, so we went with it. It has worked great so far. My wife and I were even up in the mountains with it Monday and it worked great there, too.
As far as being something fun for the family, if your kids are anything like mine, they'll love it. They're bugging us most evenings during the week to get out and do it. Even my wife is really into it, and I wasn't sure how much she'd like it.
Aside from the mountains on Monday, we've done all caches in our local parks here -- we have a few cachers who have placed a lot, so there are a ton to look for here. I'll echo winseyguy and suggest paying attention to the difficulty ratings on the caches you do, doing easier ones first. It will give you a chance to learn what kinds of things to look for when you start going for the harder ones.
Enjoy geocaching -- it's kind of addictive.