This is handy, but the good news is that if you're dealing with anything made in the last 30-40 years, it's all but guaranteed to have the ETRTO measurements marked on it somewhere.
Practically speaking there are two rim diameters you'll likely come across on all but old, "unusual" or high end bikes:
559mm: the ubiquitous "26 inch" mountain bike tire. Has largely fallen out of favor on high end mountain bikes, but there are zillions of bikes with 559mm wheels and frames sized for them out there. On high end mountain bikes, largely displaced by 29" or 27.5" setups.
622mm: "700c" road rims or "29 inch" mountain bike rims. Nearly universal on modern road bikes. If you have something else on a new road bike, you probably already know it.
Other sizes you might find in the wild:
630mm: The largely obsolete "27 inch" road rims. uncommon on new bikes, but you'll still find plenty of them on older bikes. Not even the slightest bit interchangeable with 622mm. Usually, you can't even switch to 622mm rims on frame built for 630mm because the brakes won't reach 4mm closer to the axle. Easily mistaken for 622mm if you aren't paying attention.
584mm is the "27.5 inch" mountain bike standard that splits the difference between 26" and 29". If you have this, you probably know already.
Once you've got the rim diameter right, the tire width is pretty straightforward: if it looks right, it is right. It'll be pretty obvious that a "29 inch" mountain bike tire doesn't go on a road rim, even if the diameter on both is 622mm. If you have needs under which that doesn't apply, you're probably already aware of them.
You can put hooked tires on straight sided rims safely (I have), but likely not the other way even if you could find dedicated straight sided tires.
Tubulars are a while 'nother animal, about which I know nothing :-)
ETRTO made it much, much simpler to get the rim size right when all of the various standards had different names to different people.