Fewer poles generally = lighterweight.
Non-freestanding tents might make sense for backpacking, but they are not a good choice for above treeline/mountain use.
For your stated uses, I'd recommend you look for a 4-season tent. Four season tents are built to take higher wind loads and they don't have mesh walls, or the mesh can be sealed/covered, thereby preventing snow and cold air from blowing into your tent keeping you drier and warmer.
Peruse THIS FORUM for some advice.
THIS RECENT THREAD in particular should help you out.
Regarding:
For christsakes at least take a tent out of the package and set it up in the store before you buy it.