I really dont see the point in getting LOR's from profs who just know you by saying hi to them or your grades. A prof that knows **** about you is just gonna say, "XX did well in my class, the class averag was XX, blah blah blah"! Who cares! If the adcom wanted to know if you did well in the class, they dont need a personal letter....just look at your transcripts.
For me, my LOR's came from profs who I got to know a bit personal. For instance, I am really interested in health policy, and when I took a health policy course last year, i would frequently talk with my prof, cause we shared the same interests. Not only did we talk about school stuff, but we talked about travelling, hockey (of course!), stuff like that. Even if you dont have an interest in the material, try and find other stuff u could talk about. For instance, when I was in England, I would always shoot the **** with my organic chemistry prof about Canada vs. English values, and asked him for advice on travelling in Europe, or how to get a bank account.....stuff like that. Of course this type of conversation usually came from course-related questions, but course-related questions can be used to break the ice.
There are other ways to get personal with your profs. Research is a great way! I didnt do this, but another great way is to start a conversation with a prof in his office and then ask him about his/her research....Profs always love to talk about their research to boost their ego, but be prepared for a long speech and continously nodding your head saying, "uh huh"
Sometimes I question the need for 3 LORs by schools, cause usually the LOR will be totally useless. It should be only 2 with at least one from a science professor!
Once again, just my two cents!