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If you plan to keep it white I don't think roller or spray would make a difference but rollers will have less possibility of mistakes. Kids with a spray paint unit? Not in my theatre!!! LOL

What is the wall made of?  If it is made of cement block or brick, you might need to remove flakes of paint before repainting it.  (Our maintenance man at my school could probably get the prep done for me.  It might be worth checking.)

Since most cyc curtains are muslin, I would go with an eggshell finish latex paint in a muslin color, sort of a creamy off-white, rather than stark white.  I would do eggshell, rather than flat, simply because it won't collect as much dust on it.  And get paint that has primer mixed in.  If you use fairly plush rollers, you might be able to get away with just one coat. 

Definitely use rollers.  Most roller handles allow you to screw in a longer handle, and I'd be willing to bet that there are handles on mops in your nearest custodial closet that would work just fine.

Paint in diagonal swaths, then go back over on the opposite diagonal, like a series of V's.  

A gallon of paint generally covers about 200 square feet, so you'll probably need 5 cans, or one 5 gallon can. 

You say it is a mess.  If anyone has written graffiti on it with a Sharpie, I suggest you buy a can of spray primer and cover just that graffiti with it before you start painting.  Sharpie (and tempra paint!) have a tendency to just keep bleeding through layers of latex. 

I'm assuming you actually use the wall with cyc lights.  If you don't, you might consider painting it very dark gray or black so it doesn't reflect back the lights you put on your actors.