Mask, snorkel, fins, boots are the pretty universal personal gear that people buy, normally up front (for use during the course, even).
A good fit on the mask is really important -- some people have easy-to-fit faces, others have problems. Some people like purges in their masks, others don't. This piece of gear is often really good to get from a Local Dive Shop (LDS), where you can try several on to see what fits best.
Boots and flippers aren't as tough to get a fit on, though many people pick them up at the same time, at the LDS.
Snorkel beats me. I bought a normal one, sold from my LDS, though after certification I fairly quickly put it away, switched to a roll-up snorkel that normally stays in a BC pocket.
No recommendations on brands -- I'm content with mine, though many people use different brands, all good stuff. You might want to look at some of the threads in the gear forums (and see what your LDS has).
My mask is no more than middle cost, no purge, I've been entirely happy with it. My fins were likewise middle-tier, also have worked quite well. I've since picked up a nice pair of Kinesis fins, "good stuff", just for use with my dry suit; happy with the lower cost ones as well as the higher cost.
(It's also quite possible to buy this stuff online, though for someone really new, no clue about the gear, a halfway decent LDS can be really helpful.)
Good luck -- welcome to a "gear head" sport