First thing you should do is look around for a good instructor. Speak with this person about what will be needed for your class. Odds are you will need your personal gear, mask, snorkle, fins, booties, and gloves. Everything else will be rented for the class. Out of all your personal gear the only thing I would even consider buying online is a snorkle. Would you buy shoes or gloves online without being able to try them on? Never buy a mask unless you try it on and make sure it makes a good seal on your face. To do this put the mask on your face without using the strap, if you push it on your face air will ascape around the skirt and it should stick to your face. You may have to inhale slightly through your nose and exhale through your mouth. This may be hard at times because you can not breath out through your nose or else the mask will fall off. Most people exhale though the nose you have to relearn breathing. There are several places and several ways you can save a buck or two in scuba, but a mask is not one of them. Im not saying you need to go buy a Scubapro framless mask for $125 or the Atomics Aquatics for just under that price, but if one of those two masks is the only mask that fits you correctly, that is the mask you need to buy. Dont think that you'll get an inexpensive mask now while you learn and upgrade later, buy the mask fits! If you get an ill fitting mask, it will leak on you the entire time your underwater, you will be constintly clearing your mask and not be having much fun. Snorkle" buy the simplest, cheapest snorkle you can. For one thing you wont use it that much except for class, and you going to loose it. Stay away from the super duper over engineered pingpong ball anti flood arrid extra dry with a death lazer built in snorkle. The only option that I think is worth paying extra for is if you get a flexible snorkle that can fold up in thirds so you can stick in in your pocket ~$35. Other gear: do not buy now, get certified, and get some experience Go diving and rent different types of gear. There are down falls to this, usually rental gear is not the best quality gear and people **** in the wetsuits... hopefully the gear is well maintained. If you buy gear now, you don't know what to look for and what options you will like. You might see a great deal on brand X right now and buy it, after you get some experience you might find that the stupid "dry air bleed" is really stupid and a waste of air. You might decide to get a good quality and bullet proof reg set like a Scuba pro Mk2 with a R190 second stage ~$250 and be happy with it untill you try someones balanced reg, and want to upgrade...
In short yeah you can buy gear online, you might save a few bucks, watch out as one popular site with good price is not authorized dealer of many products they sell so you get no manufacturers warantee if you buy there, but if it something that needs to fit you (mask, hood, wetsuit, gloves, booties,fins,BC) go to your local dive shop and have them help fit you.
As for getting your wife cumfortable with breathing under water, buy her a mask and snorkle and just float face down in the pool.