I'd just like to say the opposite of those who are saying that if you go away to avoid problems they will still be there when you get back.
OK, so you don't get on with your folks - you're old enough to know that by now. Staying at home and working in a dull job won't change that.
Your girlfriend? Go away for a while and I can pretty much garuantee you'll have forgotten all about her in a few weeks. What's the point in moping at home when you could be on the road?
£3000 is good travelling money. That's a serious amount of time in some parts of the world - like India for instance.
If you can work when you go away all the better. I went to Australia a number of years ago arriving with less than £500. Got home nearly two years later. Of course, the economic climate might make finding work harder these days, you'd need to research that.
The other thing I'd say (and this is possibly controversial as so many people on this forum are fun-loving easy-going 'lets get together and go travelling' types and I'm essentially just a bitter old misanthrope) is I'd be wary of hitching your wagon to anyone in a binding way, especially anyone you don't really know. I'd opt for the flexibility of travelling on my own over joining a group any day.
Get money. Leave. Simple as that.
Have a great time.
*Disclaimer* - I am not saying my bike is better than your bike. I am not saying my way is better than your way. I am not mocking your religion/politics/other belief system. When reading my post imagine me sitting behind a frothing pint of ale, smiling and offering you a bag of peanuts. This is the sentiment in which my post is made. Please accept it as such!