In reply to BenRoll:
In my opinion, probably the best thing you could do right now is try to get to know as many people as possible who are interested in what you want to do. That way, when the weather gets better you will already know people who want to get out, and with whom you will have built up a reasonable relationship with. If you find people with similar ambitions, then you will be more likely want to climb with each other, and train/prepare for certain things.
From your profile I can see you're in Leeds, a quick google search comes up with the Leeds Mountaineering Club:
http://leedsmc.org Clubs are usually a great way to learn new skills as their members are often more than willing to take people out and teach.
Leeds Uni Mountaineering Club may also be of use to you, get in touch with them, I'm sure they'll have various facebook pages and emails. Alternatively if you're heading to uni anytime soon, look for a mountaineering club there.
Regards to alpine skills, which you might already know, if not - the Jonathan Conville Mountaineering Trust run alpine mountaineering courses which teach the basics of glacier travel and crevasse rescue etc.
http://www.pyb.co.uk/courses-conville-alpine.php
I've never been proper sport climbing outside of the UK (or in the UK, really), so I can't comment too much on that, however if you just want to go climbing soon it's probably your best bet! I'd rather save my pennies for the kit and time needed to go alpine climbing!