I would recommend contacting the dive center to see what is included in the class price. Usually they should include gear rental for all pool sessions. for check out dives some include and some exclude so it pays to check. The shop that certified me also wanted me to have a weight belt and 6 lbs of weight.
For a mask you want something that fits well. Leaking masks are no fun on a dive. For a snorkel I recommend at least a semi dry, it is much better for snorkeling than a J-tube and not much more expensive. Nothing sucks more than getting salt water in your mouth from waves breaking over your snorkel. For fins it depends on whatever you are comfortable with.
Mail order is usually less expensive than a local dive shop (LDS). In state sources are Dive Gear Express (up in Pompano), Cave Adventurers, Divers Supply, Vintage Double Hose (not all they sell is vintage) and Zeagle Express. Out of state sources include: Leisure Pro (excellent prices), Scuba Toys, Dive Right Inn Scuba, Piranha, Beaver Divers, and Jim Lapenta.
A word of caution: Some dive shops expect you to purchase from them and get a bit upset if you don't. Especially if you purchase mail order or off eBay.
I agree with the consensus not to purchase anything until after you know diving is for you. I disagree with the crowd that you should rent to figure out what you want. I base my recommendation of the following reasons: 1) Expense - rental equipment is $25 - $40 per day, so it becomes expensive rather quickly. 2) As mentioned, rental gear is usually low-end and you have no choice unless you want to go from shop to shop renting gear. So your not going to be able to try a wide variety of gear or your going to try a wide variety of low-end gear. 3) The gear selection is not rocket science. Usually the best value is in the mid-priced items and in items that are discontinued or have a cosmetic change. For regulators I would recommend one with a balanced first and second stage. For a BC your choice is jacket, back inflate, and backplate and wing, whatever you decide make sure it fits. I would wait and purchase a computer last. You can always use a depth gauge and a timer with dive tables.