welcome!!! the search feature is you friend tons of answers to your questions already. I agree with the pastors recommendation, buy tools as you need them for projects then slowly expand as your abilities grow.
"leather work" covers products from car seats to watch straps, wallets to armor. you need to decide what you are going to make, that will point you to the right tools and what your needs will be
1.i would suggest you start with hand sewing because you will at some point have to learn it plus it makes more of an impression for customers buying handmade stuff. Hand sewn (wow ) machine sewn (meh) no matter which is better one sounds better and more personal. PS machine sewing is an art also that needs training and experience and a learning curve easily as hard as hand sewing.
you need to connect any leather together some how so sewing stuff is a must have, hand sewing is cheapest to start you don't need a 250 dollar chisel set you need two chisels a multi tooth and a double tooth what ever stitch length fits your project. rivets and snaps are a need. a maul or hammer, and a stitching pony. a sewing machine is a very large investment that leaves you in the red for quite a while, think how many wallets will it take to pay off, and no one machine can sew all leather, takes up permanent space in your shop.
2. stamping and tooling is optional you don't absolutely need them to make fine leather goods. So buy these as needed or when you decide to try tooling or stamping, which are kind of the same but different. I didn't tool or stamp at all for years after I started, just worked on the basic processes to make nice looking plain stuff which a lot of people prefer. I still make mostly plain holsters and belts.
3. you need finishing stuff glue, dyes, and sealers, conditioners. and a way to apply them.
4. cutting, you can get by with any number of cutting tools you probably already have in you home, knives and cutting boards etc. sharpening tools. But a strap cutter is a must imo doesn't have to be expensive but it saves tons of time as almost any project takes a strap or two it seems.
8. think outside the box when thinking about tools you can make many and probably have many good substitutes already laying around or you can pick them up at the local hardware store, flea market, yard sale, dollar store.
Good luck and welcome, post your stuff for us to see!! and ask questions.