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Buy a starter tool set. Consider some modeling tools. Get a cutting board. Get a mallet. Focus on the most important tools. Check to be sure that your tools are the best size for you. Understand the language of leather designs. Don't feel constrained to standard usages.
There's no reason to go straight into professional, expensive tools. In fact: it's best to start off with a beginners set because everyone tools differently and what works for someone else may not work for you. You want to be able to experiment. Good starter sets can be bought at very reasonable prices from stores like Tandy, both online and locally. Modeling tools, while technically designed for clay, can be extremely useful for leather crafting as well. Tools like a stylus are commonly used, as are tools like a modeling spoon. You should never cut your leather on scrap wood or any surface with a texture (and of course you don't want to cut on a surface you want to preserve), because the texture can be transferred to the leather and even make the leather more difficult to cut. You want to use a marble or granite cutting board. These can be purchased or you can ask a local contractor or granite supply company for scrap. A rubber mat underneath can dim some of the sound and keep your cutting board in place. A mallet is a universal tool that you will need for doing almost any style of tooling. You want to to use a poly mallet when you start learning to work with leather. Never use a metal mallet and avoid wood mallets (as they are delicate). Rawhide mallets are good but expensive, so if you want to experiment with these, wait until later. If you have to buy tools individually, focus on buying the most basic, most useful tools. A stylus, a swivel knife, a modeling spoon, a beveler, a mallet, and a few basic stamps (often also called single-action tools) will get you through learning the craft. Tools come in a number of sizes and the standard sizes are usually for large, male hands. If you are younger or generally have smaller hands, getting smaller sized tools will make the tool significantly easier to use. Stamps and the traditional shapes of leather working tools almost have a unique language unto themselves. Most of the tools will have names that do not seem to make sense, but almost all of them refer to the traditional cowboy leather designs and the specific purpose those tools were meant to serve. Learning the names for the tools can be extremely useful, especially for understanding instructions that you find online and for finding the tools you need. Tooling leather is just like traditional sculpting: there are lots of tools and everyone uses them in slightly different ways. You should not feel like just because you use a stamp to get one look when it's really for getting another, that you're somehow wrong. Whatever works for you and looks good is fine.