When I first started learning woodworking, I watched shows like the New Yankee Workshop and videos on Youtube. I was envious of all the tools and gears that the creators had but over time I realized that I don't work like them or build things the same way they do. The tools that I reach for my projects turned out to be different from what is often shown on the videos. To give another perspective on what are tools to consider for the hobbyist, here are what I use for almost every project.
Used for Every Project
Measuring tape - There's no project that doesn't require some way to do measurements. Even if you are going to buy rather than build, you will need to be able to measure.
Mechanical pencils - I don't recall any project that I've done that didn't require having a pencil to write or mark something. It was so common for me to be searching for a pencil that I ended up buying a bunch of cheap mechanical pencils and having them everywhere so that I don't constantly stop to look for one to write with.
Combination square - I didn't expect this to be my #1 most useful tool for woodworking. You don't usually see it being shown or highlighted in woodworking videos, but this the versatility and usefulness of this understated tool means that I use it for every project. I use it to mark, set repeatable heights, as a straight edge, 45/90 degree finder and a host of other activities. I started with a basic one and eventually knew that if I bought an high end one I'd have no regrets.
Used for Most Projects
Drill & Driver and screw drivers - Most projects will require installing fasteners (e.g. screws) so either a set of screw drivers or a power tool (driver) will be used. A drill is used for drilling holes but can also can drive screws but I prefer having separate drills and drivers.
Woodglue or Screws - Joining things together requires either glue, screws or nails. I don't use nails much so it's either glue or screws for me. For screws, I prefer the square head screws rather than phillips screws but it's not so common to find in US hardware stores. Torx head screws can be found but they might be more expensive.
Saw - Having a saw is very useful. I'd recommend starting with a Japanese handsaw which are less expensive but cuts better (in my opinion). I also find Japanese handsaws to be more versatile then western style handsaw. There are also powered saws such as table saws, track saws, circular saw, etc. Having something to cut with is VERY useful but there are times when I buy materials to size that meant I didn't have to do my own cutting.
Woodworking square - My first "splurge" tool was a Woodpecker woodworking square and I nearly always reach for it at some point when I'm working on a project. I mostly use it to check for square but I also use it to hold things square and check for straightness.
Mallet - I use a rubber mallet a lot more then I use a hammer to avoid marring surfaces when I really need to pound something.