The very first time I applied, I drew from a variety of people, anyone I felt I had any relation to at all. Professors I'd spoken with after class and during office hours; a language professor (language classes tend to be somewhat intimate); a TA... I had five letters, so the TA was more of an extra letter that I could count on for a "feel good" letter
🙂
The two semesters before I was ready to apply I became very aggressive about making connections to the faculty. Going to office hours to just talk about science in general (for science lecturers), emailing lecturers for more information about what they did, things like that. Honestly, the faculty seemed to crave student contact and they responded really well. I got to see some really neat "behind the scenes" types of things thanks to those interactions. It's almost too bad that you aren't prompted to apply earlier, if I'd known how easy it would be to make connections with faculty I might have done it a lot more and gotten more out of my undergrad...
My wife was a lot more shy about it, but she excelled in her classes far better than I did (explains why she's a med student now and I'm not

). In her case she asked people she'd worked with/under (research mentor, adviser) and she also went for a few professors that she didn't know very well, but in whose class she had done very well. In those cases the professor usually wants a CV/resume and/or personal statement. Your letter may come out sounding more generic, but hey - a positive letter is a positive letter!
Now I'm in grad school and the process is a bit harder. You know very well what the lecturers are doing, and since I have my own research project I can't really express awe and interest in quite the same as in undergrad. Luckily I have two defaults which makes the selection work a lot easier (all grad students in my program do), but the rest are open. I'll probably need to tap those professors that I don't know very well, but that I scored A's with.
It seems like one of the more intimidating parts of the process, but it's really not bad at all. Remember, the faculty are pretty used to being approached for letters of rec. It's a part of their job. Don't be shy!