By the sounds of it, you bought a house and are interested in general DIY, home renovation-y stuff.
In general, the nicer store finds are more than sufficient for that, and are used by most contractors. The needs for a machinist are way different. The box stores tend to stock a few levels of stuff, but for squares you can actually find affordable items that are nice, made in usa, and should be exactly what you're asking for.
As for individual items, off the top of my head, and depending on project: combo square, speed square, 4' T-square, rulers, maybe calipers (probably not for home reno), plenty of tape measures, various levels, and perhaps some of the other related items that will be placed next to those things on the shelves. Personally, I couldn't live without a disto and other laser levels/lines, but that's far more than the typical homeowner/budding DIY needs.
You'll notice even the nicer items at home stores aren't particular expensive, even if they're made in the us. They just don't need to be. Speed squares are just a piece of aluminum with some markings, for example. They're still plenty precise for anything you might use them for. The starrett and mitutoyo tools seems ludicrous because they're made for a different market that demands that level of precision and accuracy.
Last point: no need to get everything at once. Item number one is a tape measure (or 12).