That ISO marking means the tire is 57 millimetres wide, and fits on a 559mm diameter (bead seat) wheel. It's the metric version of what's called a 26" wheel in United States. Whether the tire will actually be 57mm wide on your bike depends on how wide your rim is; modern skinny rims will make the tire a bit narrower. You also don't know if they're measuring the casing diameter, or the extreme width over knobs if they project beyond the casing. Visit sheldonbrown.com and look for the tire articles. There's lots of good info on that site.
As for specific tires: for mountain riding I like WTB Weirwolf. They've been reliable and have great traction, and even roll decently on the pavement part of my ride. I've also done well with Specialized Nimbus and Hemisphere tires. Don't much care for Panaracer because two of them have blown out the sidewall for no good reason that I could see. There are many, many tires in sizes to fit your bike.
1989 Krapf (with Dura-ace) road bike, 1973 Sputnik (made by XB3) road bike , 1961 Peugeot fixed gear, 2010 Trek 4400
In the imperial notation (inches/feet/etc.) and in various weird notation (like french with 700C/650B/700A/etc) are all a mangle of brand marks, and do not reflect the actual size of something.
26" is just a general size.. there are at least a dozen of different 26" rims (that require different bead diameter tyre). Also french notations with 700C is something with general outer diameter of 700mm (with tyre on), and to make a distinguish between at leas 3 types that were common (622/630/635/642) thy put something like A/B/C, so 700C is 622mm. A mash of notations that do not reflect a measurable dimension is decrypted in Sheldon Brown's site, to give accurate corresponding dimension with the ISO for each weird unnatural notation.
So some guys from the ETRTO made a clever thing to put notations of the actual size and description of the tyre and the rim.
So 559mm is the diameter of the bead diameter, all tyres marked with 559mm bead diameter fit a 559rim (with some recommendations about the maximum and minimum width of the tyre according to rim width, but nonetheless it fits anyway, while a 572mm will never fit a 559).
A 559x25J rim means 559 bead diameter, 25mm width between the beads, and J is the hook profile for the tyre that fits that bead, often omitted for bikes since it's not so important and not many variation exist. For a tyre a 37-559, 37mm width of the fully inflated to nominal pressure tyre, and 559 bead diameter.
Bottom line is: Stick to the ISO/ETRTO cause it's better and manufacturers all over the world converted to that (as in always having ISO notation)
That's a good thing to standardize and stick to the same things. Some converted to metric some to imperial. Bikes are still in the imperial area with the threading on BB, on FW hubs, pitch of chains (1/2" which is great to have 1/2" on ALL chains, just as well where we have ISO notation on tyres - it removes the confusion over some oddballs and deformed meaning of proprietary notation)