If you're taking a open water course through a shop, then I have some news. You've already decided that, that particular shop is trust worthy. You are , after all, trusting them to teach you properly at a cost that you've deemed reasonable. That same principle follows through with selecting and buying the gear.
Most shops include the use of environmental suit if needed, buoyancy compensator, tank and lead weight. Most will expect you to already own and use your own mask , snorkel and fins. This part of the kit should be your first buy. The rest can always be rented anywhere in the world after you've completed the course, so you don't need to rush out and buy anything right away and can build your own kit up gradually as your finances allow. It's a great way to be still diving and yet be able to purchase some top end gear when you've saved for it and not get strapped financially.
1/ The mask. It HAS to fit. You need to try it on. Not all masks are made the same and no human face is the same. Test them in the shop by holding the mask against your face, no strap, inhale through your nose a bit and drop your hands from the mask. If it stays on 15 seconds or more, it's an ok fit. If it falls off before then, move to the next mask. Take all the ones that passed and choose your mask. Things to look for? A good quality strap and attachment points. Good visibility out of the mask, especially downwards ( it sucks to have to feel around on your BC to find items). Purge or no purge? Go with no purge. It adds cost to the mask, can get gummed up and you don't need it as you'll be taught how to clear the mask of water without one.
2/ Fins- Try on as many pairs as you can before you purchase. Everyone's kick style is different. I can't use the split fins at all. I get no place fast with them but a stiff fin like a Blade, no problem at all. Some of my pals are the opposite. Your local shop can give you guidance here and possibly lend you some demos to try in a pool.
3/ Snorkel- It has to clear easily, be comfortable and fit as close to you as possible to keep you stream lined. I disagree with the person that said avoid a curved snorkel. Most decent snorkels these days ARE curved to keep them closer to your head and make for a lower profile (streamlined). The less gear you have sticking out everywhere the better. Less chance of something getting caught and less energy needed to move yourself through the water column.
Later on, when you start buying your exposure protection (wet/ dry suit), BC and regs, you'll have some diving under your belt and will have gotten to know a few other divers and watched how their gear performs, maybe even borrowed some to try out in "real world" conditions. You'll have a better understanding on what type of gear you'll need for the type of diving you plan primarily on doing. An example would be the regs. There's no point spending the extra money on a set of environmentals that will never see cold water or a dry suit for the same reason. As for the BC, it's your back pack and your method of buoyancy control. It HAS to fit and all it's pockets , air dumps and D rings need to be easily reached. Jacket or back inflation style? Your choice, there are pros and cons for both. In a back inflation, you tend to tip face first on the surface but most people tend to be naturally in the proper swim position with no effort when under. The elastics on the air bladder sometimes need adjusting as well, to help the bladder expel air in a dump. Some back inflation BC's have a capability of being used with a back plate and double tanks as well as an interchangable bladder if it's aback inflation harness type. A jacket style floats you evenly, more or less, at the surface, but you might experience some roll when submerged, depending on your lead distribution. You also tend to feel squeezed a bit on the surface if it's inflated quite a bit. This type is generally a little cheaper than a back inflation.
Both types offer integrated lead these days, which does away with wearing a weight belt but makes the BC heavier to move around just prior to your dive. This type also makes changing the amount of lead you take with you easy to do as you only need to open the lead pockets and take out a bag from each side or for that matter, adding lead if you dive dry. Easier than fumbling with keepers on a traditional lead belt and doesn't hurt as much when you drop a weight on your toes.
Edit: It's in your best interest to purchase gear from a place that you can inspect it and have it serviced when required.
In response to the answer below me. Buying online, though an attractive price solution, is NOT the place to buy gear that your life depends on. The old saying "you get what you pay for", holds true here. Additionally, lakes can be just as exciting as ocean diving, perhaps even more so if you are a wreck diver. I've never dived a 1870's ocean ship wreck because there are none that still remotely resemble a ship. I have, however, dived many in the Great Lakes. Oceans claim ships quickly. Lake locations can actually help preserve them.