There are a couple of things to consider, cost being the main one.
Less than £300, you get what you pay for, so if you're looking to cycle quite often, it's worth buying one for a minimum £350 and you'll get years out of it, instead of having to buy another one 18 months later.
Then you've got type of bike;
Mountain Bike: Benefits are the built in suspension, so good for riders who want a comfy ride, but not exactly meant to ride at high speeds and harder to pedal, even off road, but better at absorbing the bumps than anything else. Good for fitness if that's what you're looking for. Costs are cheaper than the others, you could probably get a decent one for around £150.
Hybrids/Comfort: A mix between the road bike and the Mountain Bike. Slimmer tyres, casual riding position, no suspension springs (some do, but pricey, pricey!) but tend to come supplied with a seat that has them to make the ride a little softer. Easier to ride in parks than a mountain bike, but a bumpier ride. Decent enough as a commuter, meant for road riding/cruising, and not as costly as a road bike,will probably set you back around £3-400.
Road bike: Much slimmer tyres, built for speed not comfort. Useless off road, typically they are racer type bikes, and the riding position is something that's not suited for everyone. (I really don't like them) Good ones are about £500 and i'd steer clear of second hand, personally. But if you're looking to be a cycling enthusiast to do competitive road cycling there's not much better for you.
So it's fitness, comfort or speed. Which are you looking to achieve? How often do you plan to ride it? Will you be doing your own maintenance or getting it serviced every 6 months (usually around £75) If you are, don't use wd-40 on the chain, get proper cycle oil. Some bikes have brake blocks, others have discs, and are naturally slighlty costlier, but then you'll pay more eventually in replacement blocks over time. Oh and the only real legal requirement is to get lights, front and rear. And of course, get a sodding helmet. Ther's no official "law", but it's not worth the risk, trust me on this.
But I do recommend doing it, you will feel healthier, fitter and your body more toned. You might want to invest in a face mask to filter the air if you plan on eventually riding on roads often; i've washed mine and the amount of fine, black silt-like stuff that came out of it horrified me. Evans Cycles are in the shit, so you might get some good deals shopping there. That's all I've got for you. :)
Edit: Oh and you've got electric bikes... minimum of a grand. Fun though.
