For a beginner like you, doing laps around the neighborhood, a good starting bike would be a hybrid or an old hardtail mountain bike (without suspension). I'll second 1nterceptor's advice to find a bicycle co-op, if there's one in your area, or a bike shop that deals in used bikes. It's best to buy a bike from a shop that has experience dealing with beginners and doesn't talk down to you if you don't know all the jargon. If you post your location, forum members in that area might have specific advice for shops to go to.

Wheel size doesn't matter so much; either 26" or 700C wheels are OK. It's more important to have good tires; for a beginner I recommend relatively wide tires (26x1.75 or 26x2.0, or 700Cx35) with light (or no) tread. Inflate them to a moderate level (45-60 psi) for a comfortable ride.

If you get into cycling on a serious level, you're going to want another bike--regardless of what bike you start with--so what's most important is that you get a bike with decent components that has been assembled by someone who knows what they're doing. Avoid department store bikes, which usually have inferior components and are almost always assembled by people who are in a hurry. A new hybrid from Giant, Trek, or Schwinn starts at around $350 (plus accessories). If your budget is below that, you're best off looking for a used bike.