You are in for a treat!
Really, any salmon will work just depends on what you are open to paying. But with the brown sugar brine, you could go with something cheaper, like Atlantic Salmon. This is pretty easy to find at most grocery stores.
Sockeye is really good, as is Coho and King. These last three, are usually the most expensive, at least in my land locked state of New Mexico. I have only had King a few times, Sockeye is probably my favorite and I prefer to grill or smoke it with a little seasoning, no brown sugar brine.
I also leave the skin on for all cooks to help keep it in tact. After smoking, you can eat it or discard.
Enjoy the salmon!