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Lots of good comments! I do think it is a bit of stretch to include a jointer and surface planner on the ‘basics’ list – we’ve got a slippery slope here! And a lot of different approaches – money, space, time, resources, etc. But lets plunge ahead. If you buy your wood already (or mostly) prep’ed, then the jointer & surface planner can be postponed. You definitely need a way to accurately measure linear distances (e.g. length, width) so a good ruler and tape measure. You need to be able to measure squareness – so you need a good combination square. You need to be able to mark the wood – so a good marking knife, an awl, some chalk, a fine pencil, etc. You should have some decent chisels (and good ones don’t need to cost a lot!). You will need to sharpen them (again not expensive – piece of plate glass and some sandpaper). You need a way to accurately cut your wood – a couple of good handsaws and a file or two for sharpening. You really should have a decent work surface/work bench/etc – a good first project by the way. Last of the basics – a good drill (3/8″ vs battery type). Lastly (I could go on but room is lacking), take a look at Paul Seller’s video’s for simple but highly competent work.
On chisels, once a new comer learns to sharpen, Aldi sells a 4 chisel pack for about $20 US. They are blunt and the backs need to be flattened but once correctly sharpened, they hold their edge very well. These are my go to chisels for most work and they’re as sharp as a scalpel. My good chisels haven’t seen the light of day in over a year as the Aldi chisels work beautifully.
The very affordable coping saw (often around $20) is regularly used for rough cutting shapes in the board, but especially for removing waste from dovetail joints (one of the most common wood joints). An affordable coping saw will work just fine as long as you have plenty of replacement blades on hand (also very affordable). Read my hand saw buying guide for more detail on brands & features to look for when purchasing a coping saw.