Well, not to sound like I'm repeating everyone else, all I can do is tell you what I wen through.
I was in the same boat as the OP, was years since I last rode and the old steel Schwinn was too heavy, not enough gears and too small for me. I went to a LBS and got what I asked for, a lighter frame, upright position and more gears in the form of a Giant Sedona. I happily rode it for over a year, tooling around on the cities trails, then I started to notice that my abilities started to outstrip this new bike. I wanted to go further, out on the rodes and FASTER. The Sedona did not have enough gears, especially on the top end, not an agressive enough riding position and the twist shifters were annoying and hurt my wrists. The fat 26" tires were ideal for the suspension but slowed me way down. So I went back and bought a Giant Roam 2 - and with it I am pretty happy. It's more "road bike like" than the Sedona, more gears, larger 700C wheels, larger frame (it's toss up whether I should use a L or XL and I went with an XL on the Roam - better match) trigger shifters and hydraulic disc brakes (which I LOVE). This new bike is far better suited to me for the 100+ miles a week I now ride, rather than the 30-40 a week I rode on the Sedona.
So your needs may change if you get bitten by the "bug" an decide to ride more. If budget is an issue then like others said, look for used. Garage sales, Craig's List, Pawn Shops, heck, even a big box bike for around $100 might do, at least till you determine how you want to pursue biking. A friend at work, who turned my on to the Roam 2 after he bought one, eventually just dropped out of riding and now swears at himself when he sees the bike, gear and accessories he spent more than $1200 on sitting in his garage. He swears he's going to get riding again but never seems to find the desire.
So, decide for yourself. If you want to jump in both feet and don't mind the $$$ then go to a LBS and talk it over. et what you need NOW then reevaluate in another year or so. If you grow past the bike go back and discuss your needs and get something else.
Most of all KEEP RIDING!
EDIT: Just read TSL's post and it is superb. He's got good advice.