As NickG said, you can use Greenboard except where he noted. To expand on that a little ...
If you're going to be covering the wall with, say, surround, then you needn't prime it. You only need to prime if you're doing things to the wall that require it to be sealed from what's being 'put' over it. For example, paint or wallpaper or contact paper or whatever. If you're already putting a water-resistant / water-proof material over the greenboard, leave the board as is because if water were to get behind the material that's covering it (surround), then NO amount of priming/sealing is going to work! See what I mean?
As far as what you put 'behind' the sink, again, I'm only talking about from the countertop, on up. (At that level, you need to 'cover' and caulk to prevent water from getting down behind the countertop. Soooo, to answer your question, yes, you'll want SOMETHING installed at countertop level, on up to about 12", give or take. As I mentioned previously, get to eye level w/your faucet and draw an imaginary horizontal line from the top of it to the wall. From that point, on up for about 6", you want some protection. You can use fiberglass, tile, or the like. And caulk where the countertop meets the material you pick. Then, in short, you've protected the BOTTOM part of the wall from water. (See what I mean?)
Since you're doing this work yourself and saving quite a few $$$, consider spending some of that saved $$$ on a good Bathroom / Kitchen Remodeling Book. They're at almost any bookstore, Amazon.com, or Home Center. Reader's Digest and Time-Life both make these books. In this case, it's $$$ well spent.
My best to ya and hope this helps.
Jay J -Moderator
PS: You can search the WEB for keywords or phrases having to do w/bathroom remodeling too ...