I always preach the big five...jointer, planer, table saw, bandsaw, router table. Those are the core tools. Then add a drill press. Everything else is luxury. For hand tools, a block plane, a good combo square, a few good chisels, a marking knife, a crosscut saw and a dovetail saw. You could spend the rest of your life working on projects with just these tools and never NEED another one. The definition of NEED clearly varies from person to person. Obviously this list exceeds "just a few bucks," but this is a list of tools that every semi-serious hobby shop should really have to do quality work. There are, of course, ways around some of these tools, but those workarounds are usually a huge inconvenience and fairly often produce only mediocre results. It's not a cheap hobby. Gonna take more than a few bucks.
I know you guys are talking power-tools so I'm a bit off topic here - but just for giggles I dug out all the tools I used to make my first project. Not pictured is the cheap knock-off B&D workmate bench. Using S4S lumber took care of all the heavy milling (at the time I didn't know you could even buy rough lumber). Add consumables like glue, sandpaper and finish and that's all. The whole lot (including the wood and consumables) cost about $300CAD - my biggest expense after wood was probably clamps... For my second project I added a router (power!) to do fancier joinery, and more clamps. Before the third project I built the workbench and then acquired some hand-planes and saws so I could mill rough lumber. By my fourth project I was right down the hand-tool rabbit hole and started gathering joinery planes etc. And soon after that the addiction had bitten deep enough that cost isn't important - I know what I want and pay what I have to to get it. So why didn't I start out with power-tools? The short answer is that it never occurred to me that I should. The only people I had ever seen using power-tools were professionals, all the amateur woodworking I had ever seen, either dad at home, or in school woodwork classes was all unplugged - it just happened to turn out that I prefer it that way. So I'm not sure what my advice to a new beginner would be, probably not very useful. Buy some wood, use whatever tools come to hand, don't stress, and have fun.