Chemicals:
Developer (whatever you choose, it is always good to experiment.)
Fixer
FotoFlo (a super soap type stuff for your final rinse)
Optional Chemicals:
Hypo Clearing Agent (a liquid chemical which removes fixer, shortens wash time)
Hardware:
Gallon Jugs (2), one for developer, one for fixer
Thermometer (1)
Graduate (1), just easier to have a dedicated utensil in one place than using your food measuring cup.
Development tank (1) I suggest stainless steel tank and reel(s), tougher to learn on but uses less developer and one gets better circulation.
Optional Hardware:
squeegee (fingers work fine)
film clips (weighted clips for use when drying film, clothes pins work also)
changing bag (a light-tight bag used for loading film from cassette to reel, otherwise you gotta find a 100% completely dark room)
film washing tank (a cylinder with a hose attached which you drop in your film reels, gives a better wash than a developer tank wash)
film dryer
Important:
When air drying film, choose the most dust free area you have available. Typically, the bathroom is the most dust free area in the house.
Good Luck,
Gary