Microscope for phono cartidge

Personally, I wouldn't go with anything less than a 50X, although for a hand held, it is easier to find the stylus in the scope with lower power.

I tried the "kiddie microscope" route but these don't elevate high enough to place the cartridge on to the slide area.

I purchased a 30X hand-held inspection scope that did the trick. Make sure it comes with a plastic snap-on fixture to hold a fixed length (away from the stylus).

You are looking at the general condition of the stylus.
Make sure it looks close to new and, especially, that there are no flat spots on either side.
the stylus and shaft should be symetrical and not leaning to the right or left.
Inspect the suspension and make sure it's not dried out and/or cracked.

Go over to the vinyl engine and look at "nude pictures" there is lots of info. The cheap usb scopes work but have a limited depth of field which can be overcome with software but is kind of involved. You can score a nice B&L stereo 70 for around $300 on e-bay but you also need a good light (around $150) I love my stereo 70 we use it for bugs, gems, boogers, you name it. I got it to examine stylii but now the whole familys into microscopy.
p.s. ticks are especially gross

I remember seeing a kid's toy electronic microscope - inexpensive and very worthwhile for stylus examinations. I don't remember where I saw it, but check toy stores or Google.