Should I "offer" something when asking for a letter of recommendation? I'm an undergraduate and currently applying to summer research programs that ask for letters of recommendation. Last summer, I did research at a university with a professor who I'm planning on asking for a letter. He mentioned how he would like more people who are studying computer science to apply to his summer program, so I was thinking of telling him after the request for the letter that as a token of my appreciation, I would be happy to encourage people in the computer science department to apply to the program.

Another professor who I was considering asking is thinking of teaching a course in the fall that I want to take. I was also thinking of asking him following the request for the letter of recommendation about whether he is still planning to teach the course and that I would like to take that course with him in the fall. 

My intention is to give something to get something even if both professors would most likely write me a letter regardless of whether or not I "offered" them something in return. Are these things that most professors would appreciate, or do they sound too business-like and Machiavellian (in that they are part of an email asking for a letter of recommendation)? Should I just straight up ask for the letters?
Just straight up ask for the letter.  There is no need to "pay back" with some favor.  Writing letters of recommendation is part of a supervisor's job.  However, it would be wise to include in your email:


Position description so they can describe the most applicable aspects of your prior work in their letter
Ask if they would be willing to write a "positive letter of recommendation" because if it is not positive, they should not write it
Information about: where to send the letter, to whom it should be addressed, and the date when the letter is due
Ask if they would like you to send a reminder email 2 weeks and also 2 days prior to the letter of recommendation due date


Additionally, if it has been some time since you spoke to this person or you do not know if they remember you, include your latest CV or Resume with your email. You should never have to draft your own letter of recommendation.  I highly look down on this practice, though you may encounter it.