Fly fishing is no different than any other hobby in that enthusiasts can tend to get obsessive about their equipment. While some fly fishermen probably take it to the extreme, equipment is very important and contributes to comfort while out on the water, limiting frustration, and having a successful day catching fish. If you make good equipment choices you're more likely to have an enjoyable experience.
Rod and Reel
The first and most important advice regarding rods and reels is simply to buy the highest quality rod and reel that you can afford, as long as it meets your needs. While you can get away with skimping in some of your other equipment needs, your rod and reel are not the place to do it. You will be unhappy and ready to chuck a cheap rod or reel after you gain some experience (often after just one or two fishing trips), and will be spending that money again. Skip this frustration and buy gear that is made by the most respected makers in the sport. Look for rods by Sage, Loomis, Scott, Powell and Winston. Some reel manufacturers known for their quality are Ross, Abel and Sage. If your budget is tight, it is better to buy a used rod from one of these makers than a brand new cheapie.
Waders have evolved from all-in-one heavy rubbers with boots, to neoprene, to comfortable and breathable models that are lightweight. Consider going with these new breathable waders. They are very comfortable, and the fisherman feels very little restriction when wading. They come on and off in a breeze, as easy as slipping on a pair of sweats. The fact that these waders breathe means that they prevent any clammy feeling and actually keep you cooler in the summer and warmer in the winter (there is plenty of room under the waders to layer-up in cold temperatures). Prices are affordable, so there is no reason to not have a pair.
The right accessories can make a big difference in convenience and performance while fishing. A magnetized net keeper on the back of your vest makes it much easier to pull off and put back your net, eliminating the twisting and turning acrobatics that are usually necessary. Try a pair of polarized sunglasses with amber color lenses and you will be astonished at your ability to see under the water and spot fish. Polarized lenses are designed to take the glare off low light conditions like in the early morning and late evening.