A good set of 5-7 bench chisels (they don’t have to match) will get you going right away. Down the road you’ll eventually add some specialty chisels (like paring chisels, fishtail chisels, etc) but bench chisels will work for just about everything. I often pay only $10 for high quality vintage chisels, so a compiled set can certainly be affordable, and higher quality than low quality new sets. Read the chisel buying guide to learn what chisels to avoid and which chisels will work great.

I work with a lot of rough sawn boards (Wood Mizer) that are up to 12 inches wide. The worse defect is twist. First I saw the stock to rough project lengths and then using winding sticks, I attack the twist with a #5 hand plane, gradually moving the winding sticks toward the center. If there is bow or cup I can plane that out also. I now have a reference surface that can go thru my planer. The finished boards are perfect. This is not really difficult or excessively time consuming.
Most of your cutting will be done using power tools. While you can go full neanderthal and work solely with hand tools, modern power tools will make your woodworking hobby much more enjoyable. And you don’t really have to spend a fortune to get them. For some of them, you can easily find low budget alternatives. You can also ask your wood to be cut at the store you are buying it from.
My $0.02 worth. I agree with the thickness planer [mine is 10″] but anything over a 6″ jointer is expensive and space-consuming, so use hand planes as in your later blog. I inherited an 8″ table saw that my dad and I used to build a 12′ outboard boat back in 1955. I’ve used it for ripping, but I’m having second thoughts because of safety issues. Some have suggested a band saw for ripping, which is quieter and safer to use. I gave my router away [and hope to get rid of my Freud biscuit joiner and 6″ jointer]. A quality eggbeater drill works every bit [pun not intended] as well as a power drill, and they cost less. A coping saw and a jewelers saw negate the need for a jigsaw unless you are into making puzzles. Chris Schwarz has a video short on one of the Highland Woodworker series showing how to joint the edge of a board with a plane and a simple jig on the workbench surface. Another reason to bypass the jointer.
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!
The third tool for the beginner is the Jigsaw. A jigsaw allows the user to cut curved and circular patterns in stock. Sure, a band saw will likely be more accurate and can cut thicker stock, but for the beginner, the jigsaw (sometimes also referred to as a Sabre Saw) can be perfectly effective. For versatility, choose an orbital-action, corded jigsaw that feels good in your hand and has an easy blade changing system.
To start off you only need either a 1/4-inch or 3/8-inch mortise chisel (or some size close to those). I prefer 3/8-inch. You don’t need a whole set of mortise chisels. Mortise chisels (also spelled “mortice chisels”) are used for chopping mortises (rectangular holes) into the side of your board to accept the insertion of a tenon. “Mortise and Tenon” is a very common and very strong joint that most people have heard of.
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.