What format are you working with? I will assume it is 35mm since you sound very new to Fine Art Photography. Processing film is just like following a recipe, easier then baking a cake. If you can do that, you will be a wiz at it.
You will need a tank, some reels, two plastic containers, one for your developer, the other for you fixer, thermometer, a light tight room, or a changing bag, bottle opener. Most of this can be purchased from a local photography store, or go to Calumet.com and search there. I recommend you buy all equipment new. Used reels and tanks may have been dropped and will bend or warp, making them useless. A Kodak glass thermometer is a good one to start with. Get a 2 reel 35mm tank and 2 reels to start with.
A changing bag is essentail if you do not have a darkroom since it will allow you to load the reels in total darkness. The smallest size will be fine for your needs.
I personally use stainless steel tanks and reels. I recommend you practice first with a dummy roll of film you don't care about, loading the reels first in daylight then in the changing bag. Practice until you know by feel, without looking, that the film is loaded properly. It is a little difficult at first, but once you master stainless steel tanks and reels. it's like riding a 2 wheel bike.
Chemestry I recommend to start with is Kodak D76 for developer, and Kodak Fixer (the powder form), and Photo-Flo which is a wetting agent so your negatives dry smooth and clean. They are easy to mix and give good results and can be bought in half gallon sizes.
You can also take a photo course at your local community college, or find someone teaching with a beginners workshop or adult ed. There are plenty of beginners books out there, The Zone VI Workshop, by Fred Picker is very helpful. Start at your local library and pick up a few beginners books.
Welcome to B&W photography, it is an addiction that will improve your health.