My friend said I need to spend at least ￡225 to buy a "good" bike and that anything below would rust too much. I wanted to buy one for ￡115, is he right..?

Depends what you're using it for.

Off-road?

Commuting?

Just to get to uni.. in London..

Just to get to school with? Get whatever is cheapest man.

From what I know of London, there's always a chance some deviant will try to have six with it, so it's best to get a cheap one.

I got my first bike as a present I asked for when I was 10, it only cost $100. It still works fine and I ride it to get to the gym.

Pretty much guaranteed that if it's not going to participate in some hideously perverted act, it'll be stolen, driven over, vandalised, eaten or turned into a piece of modern art. Or all of the above. So cheaper is probably better.

What's best..?
There are 3 to chose from, mountain bikes, hybrid and racing..? Hybrid I guess..?

It's really down to how much you're going to use it. If you're on it everyday and you're going to maintain it, then a ￡100 bike will do you. Many series bikes ( usually mountain bikes ) share the same frame, the pricey parts are the components, and if you don't maintain it they're going to fall apart. Hybrid are generally commuting bikes with small suspension rigs. Racing is it's own league really and they can be dangerously expensive. It'd only buy a mountain bike for the city if it was a decent hardtail (Hardtail means no rear suspension) that I could slap slick tyres on.

Can you show us the bikes you're interested in?

how do you still fit on a bike you got when you were 10