i have both the thick and thin parallels
the thick ones are nice when working on larger pieces in a vise, the thin parallels are sometimes useful, for smaller work so the jaws of the vise can close more.
both are valuable to have, although the thin ones are a little more versatile, but a bit more of a PITA to use sometimes
Precision machinist levels can be very expensive and can have resolutions of .0005" in a 12" span
i have a Blanchard Level that is .0003" in 12"
if you are vigilant, you can find old Starrett spirit levels for less than $125
an 8" or 12" level would be preferable, but 6" levels can be useful too