My approach was always to make sure your professors know who you are. This means asking additional questions after class, engaging in conversations about the subject or anything else. I’ve made friends with professors and when it came down to asking for LORs, many were quick to say yes. This even happens with a class where I didn’t even do well but became good friends with the professor and a really good letter of recommendation came from him.
At the same time, I had one of the highest grades in another class and was doing everything to be recognized in that class. Yet the professor refused to write me one. Her excuse was that it is better for someone to write a letter who knows me more??? Seriously, one semester isn’t enough to know a student? Most students you’ll only see for one semester if it isn’t the same teacher teaching the advanced sciences.
I’ve never had to provide a packet or resume for any of the professors I’ve asked. One barely knew me and still said yes and just wanted me to give a little background information about myself sent through email which he’ll then use to write based on. So this might be something they will ask for. Plus you can always ask if a packet or resume is something your professor will need.
I’d say ask all of them, even the ones who might not know you well. If you need 2-3 LORs, go to the professors that will say yes for sure, then ask the rest. Trust me, you’ll be surprised at those who may say yes. If I was a professor, I would be honored to write someone a letter of recommendation because it means the student values my opnion of them.