Depeding on whether you plan on brewing an all extract brew, an all grain beer or some combination of the two equipment plays a key part of brewing. There are also some considerations that should be taken when brewing different size batches. This page will list out the bare minimum equipment first then list some optional equipment based on what you plan on brewing.
Typical batch sizes for home brewing are 2.5 Gallons and 5 Gallons. If you are just beginning to homebrew it is recommended that you start with a 2 or 2.5 Gallon batch like the one that can be found in our tutorials section. A 2.5 Gallon batch allows you to brew about a case of beer or 24 twelve ounce bottles. This also has the advantage that if something goes wrong, you don't have to suffer through to much of your brew, or if something goes horribly awry, you didn't waste too much money on your brew if you have to dump it. A 5 gallon batch is best if you have a better idea of what you are doing or have some faith in your recipe. A larger batch also lets you share some of your delicious concoction with your friends. Keep in mind however, the batch size can increase to whatever size your heart desires (and whatever size your equipment can hold.)
When dealing with a 2.5 Gallon batch you don't necessarily need special equipment to brew. The brew pot can be a simple kitchen pot, your stirring spoon can be a simple tablespoon, and quite possibly the best fermenter to use when just starting would be a standard bottling bucket. Using a bottling bucket as a fermenter allows you to bottle straight from your fermenter, which can be very convenient for a beginner.
Now for a 5 gallon batch you might want to consider investing in a large stainless steel spoon,if you don't already have one, for stirring your larger batch. A pitcher with volume markings is also a good investment for measuring the large quantities of water you will be needing for your batch.