Jackson C.
Yelp
If you're looking to learn basic alpine climbing techniques, the Mountaineers is an inexpensive and effective way to go, but the low price comes with some drawbacks.
One is that it's a club that has to teach protocols that convey insurance coverage to certified climb leaders. The structure and hierarchy bleed a certain amount of the fun and joy out of what should be recreation - when I was in the class, it felt a bit like a job. The basic class seems to be viewed by most students and instructors as a precusor to the intermediate class, rather than an end in and of itself. There's also a culture of assessing performance, which leads to some sense of striving for informal standing and status. In short, it's not a particularly fun environment.
The courses are volunteer-run, so you also have to put up with inconsistencies in techniques being taught and tested at times. Instructor's people skills aren't always the best.
As a club, they have rules, and as with any rules, they can feel arbitrary (for instance, they just started allowing students to bring rock shoes to use on rock climbs instead of insisting on mountaineering boots only and they just started allowing lighter-weight wire gate carabiners instead of standard ovals - despite these changes, I'm sure there are other rules still in place that current students won't like, such is life).
All that said, I personally learned skills that I now use in the mountains - self-arrest, self-belay on snow, navigation. I got on rock for the first time in their course and found I really liked it (although others who just want glacier skills bristle at having to do rock). I did gain "the freedom of the hills," which in my case meant gaining the skills and confidence to summit a whole series of peaks I'd never quite finished.
So as long as you can look past the drawbacks or if your personality is just well suited to the culture of the club, it's a good way to go. If you're independent-minded or if having a good time when you climb is crucial for you, you might want to look at short courses and other options.