Your list is pretty decent already, and will get you most of the way to anywhere, assuming you also have standard things like screwdrivers, a hammer, tape measure and a ladder.

The thing about "general work around the house" is that it can mean anything, so the best thing to do is just buy your tools as projects come up. For example -- I had to replace the subfloor in a laundry room, after the washer leaked and the existing particle board subfloor absorbed all the water and deformed. That's when I upgraded my anemic cordless circular saw to my current one, and bought a pry bar (because trying to use the claw end of a hammer sucked). So now I have a pry bar in my arsenal of tools for general work around the house. It's nice, but certainly not something I'd say, OMG, you *have* to get one of these -- because the truth is, you can get by just fine without one for years. And that's really true of a lot of tools. My non-contact voltage tester pen, (crappy) chisel set, mitre box and cross-cut saw, level, hacksaw, aviation snips, and a host of other tools arrived similarly.

I think I have 5 tools that I bought "because I should have these", rather than "because I need it for my current project." Two table saws, a router with router table (it was a good deal at a garage sale), a belt sander, and a pair of drywall T-squares. Of those, I have only ever used the drywall T-squares. The rest just take up space in my garage.