I consider this my “basic” tool list. Although I do not have a dedicated box for these tools, I assure you that they have a great home in cabinets, on shelves, and laying around on benches. When I do need to take my hand tools somewhere, the larger tools end up in a simple tongue and grooved latch box my grandfather owned. The smaller tools are always in my overall pockets. Overalls work great. They have multiple pockets, they’re comfortable, and they protect your upper body and legs. You only have to deal with small chunks of wood getting into the pockets, which can be dealt with if you or your other half are crafty enough to sew some flaps. It doesn’t bother me though. Thanks for your time.
If I were to give someone new one piece of advice, it would be to buy their chisels new, not used. I have wasted more time and more money trying to save butchered chisels than I want to admit. There’s a good chance that the used chisel will be bellied in the back or pitted at the edge and it will take more than beginner skills to fix it. You may make things worse rather than better. Sure, learn to do this _some_ day, but maybe not as a beginner first thing. I’ve had similar problems with used planes, but it isn’t nearly as bad a problem for a joinery plane. If there are pits that lead to scratches, it may not matter for anything other than a final smoother. Also, a tiny back bevel may save the day on a plane, but you likely don’t want that on a chisel. So, I’m less fussed about planes and, if it all goes south, you can buy a new blade for smoothing work and use the old for rough work (all in the same plane). You can’t buy a new blade for a chisel. Well, you can, but it’s called buying a new chisel. I use 3/8″ a lot. 1/4, 3/8 to handle all the mortises and dovetails and either 3/4 or 1″ for paring shoulders and for fat parts of some dovetails. I probably learn towards the 1″ because there are times you want to reference off the blade to keep moving in a line, like for a housing. I think Lee Valley’s version of the Narex are excellent and mine came with flat backs that could go straight to polishing.
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.
In the sixty years of woodworking I have found two tools of increasing necessity. One is a band saw. I can do most of my work with a band saw and hand plane. The second tool is a bow saw, or actually several bow saws. They will replace the band saw if required, though they are slow. One I made about twenty years ago has a one and a half inch wide rip blade and is about thirty inches long. I think the blade is from an old industrial band saw blade I picked up and sharpened into a rip saw blade. It works very well on ripping lumber, logs, etc. Though it tires me out to much to use it now.
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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.

Rabbets are one of the most common joints in furniture making, so a handplane that cuts a rabbet should be toward the top of your list of tools to buy. Yes, rabbets can be cut without a handplane, but at greater difficulty. I own a lot of handplanes that cut rabbets, including wooden rabbet planes, metal rabbet planes, shoulder planes, and moving fillister planes. While I use all of them for specialty tasks, I find that a metal or wooden moving fillister plane (pictured above) is the most useful, as it allows me to cut rabbets with the grain, across the grain, and allows me to easily cut panels (as seen above). And the movable fence helps greatly with accuracy. I discuss rabbet planes in great detail in the handplane buyer’s guide.
about three years ago I thought to make even only a cutting board I would need a complete set of machines, stationary and handmachines, plus of course a few handtools for “hybrid woodworking”, then I discovered Peter Sellers and most importantly Chris and The Anarchist’s Tool Chest, that was a revelation! So I find it absolutely awesome that you show us how to start with even less tools (especially the advice for saws is great, much cheaper to only get rip)!
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Dividers (or compass) are used for taking and repeating a measurement over and over again on a work piece. Traditional woodworkers rarely take measurements with a tape measure when doing fine joinery work, but rather take a measurement with dividers then transfer that arbitrary (yet accurate) measurement to another work piece. This removes a degree of inaccuracy.
I use chisels perhaps more than any other tool in my workshop, so it’s a good idea to not cheap out here. A high quality set of bevel edge bench chisels (new or vintage) will last you many years (likely  your entire life) and will be used on nearly every project. I’ve used some descent affordable plastic handle bench chisels, but highly prefer lighter wooden handle chisels with excellent steel.