I want to add another wrinkle to the whole getting into alpine climbing thing. For me, building the excitement and absorbing certain useful attitudes came largely from reading some interesting books. Of course, those old classics like "the White Spider," any of Hermann Buhl's books, etc. But this one is really good:
The Boardman-Tasker Omnibus
4 excellent book-length expedition stories in all kinds of harsh conditions. Sadly, the authors died climbing, but they left behind an amazing record. There are a lot of other good books too, just thought I'd mention this one as winter is coming on and you might have some evenings at home to read.
I don't know how many other "sports" can draw you in via literature like climbing can. Maybe sailing.