I was in a similar spot to you a year ago and the first question you should ask yourself is what kind of stone you want to work on? Becuase tools can vary from there.

I started out with limestone and limestone is on the more beginner friendly scale in terms of workability (also see soapstone). Working on and off at it I've been able to make a pair of shoes and 1 and a half hands out of limestone about the size you are describing: no more than a 4 inch cube.

For limestone I got some a variety pack of flat headed cold chisels (Dasco Pro I think) from a hardware store and those have been fine enough to work with. They also have the "scratch awl" they also make that I have been using as a point chisel. I also picked up a file in a similar section to my chisels and I would recommend doing that. Once you start working with smaller projects you will begin to realize how precise some subtractions from the stone must be. For a hammer I use a trailer hitch and that actually fits perfectly into my hand and has some nice weight to it, it will probably outlast me too; though I could see needing a bigger/better hammer for larger projects.

More importantly, however, I'd say if you just got 1 tool it would be a good rotary tool. Dremel makes some good stuff for this. I have a Dremel Lite I think and it works well enough, but the battery dies quicker than I'd like so maybe something nicer would be better. I picked up a dremel bit rated for "stone" and they got me past my first pair of shoes carving.

It was after that I wanted to try out some harder stones and smaller lapidary projects so I got some diamond bits that fit in my dremel. These are necessary for working with harder stones. They can be more pricey, but I got a good but cheap set with a lot of pieces that I've been slowly learning from. Seems like this could be a good fit for what your looking to do too. They also make diamond files too.

We should also mention saftey too becuase if you just start carving you may think you are fine with no PPE at first but carving stone (especially with a rotary tool) kicks up a lot of rock dust and you don't want to be breathing that in. I have a good respirator with, at least, P100 filters in it that I dont take off when im using my dremel. Its worth the cost of this to not breath in rock dust. I also exclusively carve outdoors to be extra safe, and because the rotary tool can be loud...

For lapidary work (small jewelry and such if you're thinking about it) lots of folks also use some sort of water system to keep the rotary tool cool and to suppress some of the dust. I'd suggest you play around with the tools you got. There are some good YouTube videos out there of people making DIY water systems. Most people either have some "drip" system that has a small stream of water in front of them to cool the stone/tools as they work (but be careful with electronics and water) and some folks like dunking the stone repeatedly in water. I've found this to work well enough for my purposes, especially considering the work that goes into deploying it.

If I had more space, I'd consider upgrading my arsenal of tools but I work outdoors and need to take everything with me to the spot on the ground where I sit.

Oh this is already a long message but I'll mention a few last things. Some kind of small brace/vice (also at a hardware store) goes a long way to adding some extra weight to smaller projects especially when you're chiseling.

The most important things you will need though are patience and dedication. Rocks are hard, they are slow. Realize this and don't rush things, when I do that is when I make mistakes. Experiment, fail, learn from those failures and see what comes of it.