Many beginners trying to get started in woodworking take one look at their budget and worry about how they can afford to buy a whole shop full of power tools to get started. Fortunately, one doesn't have to spend a fortune to get started. There are really only seven woodworking tools that I would recommend any beginning woodworker have on hand from the start, and most are relatively inexpensive. However, with these seven tools, a beginner can tackle quite a number of projects.
Like yourself, I get great satisfaction from working with this small kit. Similar to your wine box, I’ve got this old ‘sausage box’ that I can fit everything in, if I’m out the job site or such. It’s a lovely feeling to know that with just this small box of tools, I can pay all my bills and eat. I just wish I could get the rest of my life so minimal!
Wooden mallets are mostly used for hitting your chisels when cutting joints (like dovetail joints or chopping mortises). You should never hit a chisel with a metal hammer. Build or buy a mallet that is made of fairly hard wood (e.g. maple, oak, beech wood, etc.), that will feel well balanced in your hand, and that gives you enough weight to chop with your chisels.