In reply to Mr Fuller:
theres good and bad sides to gyms and its all in your head. treat the place as a virtual environment and it works, but get caught up in the hype and it starts to be about the gym and not you.
id mix it up a bit: alternate 'top end' lifting with 'baseline' lifting. so some heavy stuff for 3 reps and some light stuff for +12 reps. maybe a 2:1 ratio each session (2 of one to one of the other, maybe 6 lifts per session).
the light stuff you could do with just a stretch bar and on a balance platform.
5 lifts? front squat, clean+jerk, overhead squat, standing row, deadlift.
all of those could also be done with DBs or KBs.
none of that really is direct climbing stuff, rather its for strengthening the bits that make general climbing easier.
get some good shoes for that as regular trainers are crap. barefeet is ideal for learning if the gym allows it (good luck).
another angle is to do your lifts then 90secs of hard cardio effort straight after.
mountaineering specific training in a gym i think is only about 50% to do with bar bells. the rest is about +body weight, range of motion, output, body integrity and complex stress.
unless you feel like it, theres no need for any of the machines except maybe one or two cardio things like a treadmill or rower so you can guage speed/kcals/etc. dont get dazzled by all the levered junk, learn to blindspot the stuff that you can do better without.
and if your gym does bellydancing classes, find out when they are. its easier to train when the place is full if girls with their navels showing and their hair out.