I took a course in Montana in 2012 that was offered in the rec center at the university where I worked. It was very helpful. We at least learned basics like how to tie ourselves into the harness, how to belay, and a little bit of info on technique. I still wouldn't feel comfortable going outside on my own (the class was indoors), but I'm glad I got that start.
I took three courses in a gym, the first was the starter course (how to top-rope belay), the second was how to lead climb, and the third was how to climb multi-pitch. All courses were great, but the instructor for the lead climb course was exceptional. As you get into climbing more and more, I do reccomend more advanced courses, because you get to learn from experts in the craft, and they get to share their passion with you. Its educational and inspirational.
Yes, in college I took intro to climbing, lead climbing, multi-pitch, trad anchor building, and intro to mountaineering courses. Then I climbed outdoors quite a bit with mentors. Having mentors was key for me. They gave me specific advice and one on one instruction was invaluable. Three of my early classes were taught entirely outdoors, which also helped me be immediately comfortable climbing outside. I really wish that it were easier to find skill set specific classes now that I’ve been out of college several years. The gym in the town I live in presently openly states that they don’t hold any events, which is a bit disappointing. But bottom line: I’m glad I found the time to take all the classes I could, and would live to take more!
Yes, I took a basics course at the gym to learn how to belay properly, as well as how to stay safe as a climber. I think these basic courses are great and everyone should take them before climbing.
Beyond that, before going outdoors I recommend finding an experienced group or mentor, and spend a lot of time with them. Outdoor classes (anchor building/multi-pitch/etc..) are great, but they don't cover everything. Having a group to watch over you is invaluable when dealing with such high consequences of failure. Having someone experienced there to stop you when they see something wrong is more valuable than going out with a pal who took the same course as you...
I think most areas have organizations... if not, check the craig you are planning on cilmbing at and find one associated with it.