Yes, yes, yes, and yes. One thing you'll find across all of the message boards here is to just do anything you can find a position doing. The more a stage manager knows about each element of production the better.
Does your department allow you to work on more than one thing at a time? I've found it really helpful to, say, be on electrics crew for the same show I'm SMing--that way, I can have a conversation with the LD about what look this light is a part of, what scene it's for, why this kind of light, etc--and then when I'm calling the show I have a really good picture of what each type of light looks like. And that works in all aspects of the rehearsal process, from props crew to direction to costumes, sound, etc.
All of that said, pick whichever one you have the most interest in to start off, or pick an area you have friends in--I don't know that I would recommend any one "other" role over the rest. You may find a second passion simply by spending a semester on a new crew.