I really asked the question to try to distinguish between lenses that are great performers from those that are poor.
Personally I am not interested in optical formulas and the math that goes into the design. I am more interested in when choosing between the lenses which is the first choice, second and so on.
I think the only way to answer *that* question is through your own experience. Quality is so thoroughly subjective, and our vocabulary for talking in lay terms about optical properties is so limited, that it's hard to see what could be said about lenses that would help you in these terms.
For what it's worth, here's how my brain organises lenses: The most basic reasonably modern lens is a triplet, which occurs in a million different brand names with essentially the same design. Novar, Triotar, Cassar, Trinar, Vaskar...
Triplets have the basic problem that away from the centre of the image, especially wide open, they tend to go soft and vignette. Hence the Tessar design and its close kin, which add a fourth glass element to reduce these problems. Again, in addition to the Tessar itself (which was a Zeiss trade name), there are a bunch of essentially similar designs; Xenar, Skopar, most or all of the Russian "Industar-nn" lenses, etc. Unfortunately many of the same names have also been used for lenses of different (often *very* different) designs, so the name per se isn't a reliable guide---you have to have some context in order to know what lenses the name was being used for in a particular time, place, and setting. (The Lens Collector's Vade Mecum is helpful for keeping track of these changes; it's imperfect but it's still a helluva reference.)
I believe some of the Leitz Elmars are Tessar designs.
You can, of course, keep adding elements and changing configurations in an effort to climb the diminishing-returns curve; Tessars are a lot better at the edges than triplets, but there's still room for improvement. The canonical "next step up" from the Tessar is the Planar, which adds some more glass, is sharper, vignettes less, and costs more. Schneider's Xenotar, mostly seen on Rolleiflexen, is similar. However, things get complicated here because the number of reasonable combinations grows as you add more elements; five or six elements is enough to create a lot of design flexibility, and except for a few well-known lenses (Planar, Heliar...), it becomes difficult to use the name as a guide.
Also, it seems like the tendency to use the name as an indicator of the design went out of vogue sometime in the latter half of the last century, leading to things like the Olympus convention where a prefixed letter tells you how many elements there are ("D.Zuiko"==4 elements, "E.Zuiko"==5 elements, &c.).
And then Leica lenses are a language unto themselves, with the name sometimes reflecting the design, sometimes the maximum aperture, sometimes apparently just a whim. I've never attempted to understand this part of the lens world, as I don't ever expect to be able to afford an actual Leitz lens.
Finally, there are some outliers like the Zeiss Biogon (and its Ukrainian clone the Jupiter-12), which don't fit easily into any particular schema and just sort of have to be treated as individuals.
But as far as what you *like*---that part you gotta take up with yourself. Some people really like lenses to be as close to technically perfect as possible and will happily spend the GDP of a small country for a 237-element monster made of unobtainium-tinged glass hand-polished by elves enslaved in the forges of Mordor, or whatever---others find the theoretically "best" lenses to have a sort of antiseptic look and actually prefer using ones that on paper are "inferior".
-NT