How far do you want to go? Stephen Howard's Haynes Saxophone Manual is a great starting place and tells you what you need to do the different jobs.
Minimum (imho) is a pull through for inside the body, soft cloth for cleaning the outside, a brush/pull through for the neck, and cork grease. If you want to go further, adjusting keys, then a set of jewellers screwdrivers will do most of what's needed. To start with the corks/felts a supply of cork sheet, felts, shellac/glue, very sharp knife (think old fashioned razor blades) and fine wet and dry (400, 600, 800, 1000 grades). And some smooth faced pliers, for bending keys. Springs need more round nosed pliers and a spring remover. For pads add in a set of pad slicks and a small spirit lamp, or small gas torch that's easily controllable and will shut down to a low flame, and a pack of cigarette papers or a leak light.
But it's all in Stephen's book.