I just got a bike a few months ago having not ridden since I was a kid. I asked some bike-freaks at work for advice and this is what they told me:
- get a second-hand bike, you can get great parts for less, whereas new bikes are like new cars, extremely overpriced.
- make sure the brakes (and gear parts) are metal, plastic ones have a lot of give and get wrecked quickly.
- have a quick look at the shimano (or SRAM I guess) gears range because they have a bunch of different 'levels' for their parts, and the budget ones aren't very good at all.
- make sure you get the right size for you, there are plenty of measuring charts online.
- don't get a full suspension bike, the good ones cost a lot. Even bikes with front shocks are unnecessary unless you're hitting trails hard.
- get an aluminium frame if you have to carry the bike anywhere. Someone also told me they ride better.
- don't worry about mudguards, tires (the rubber), panniers, racks, or any of that other periphery crap, you can buy them separately for cheap.
That's about all I remember, but I ended up with an awesome bike that rides superbly for €100. It was top of the range about 10 years ago, and as it hasn't been used much still feels like a great bike.