Best LPs to Test Turntables

Its pretty simple. Bring what you are familiar with, that are well recorded, with music you like, and won't mind playing a lot, letting other people handle, etc. One will do, initially. Then if you narrow it down to one or two and its close (unlikely, but you never know) bring a few more, representative of what you like to play the most. You are after all buying something to play to please yourself. Keep that in mind and don't go trying to impress anyone with your audiophool cred. 

Perhaps not quite that simple.  Start with a good solo (or small ensemble) piano recording and listen for excellent pitch stability.  Listen carefully to the decay of notes or chords at the end of musical phrases.  Do you hear any pitch waver as the note decays?  If you do, move on.  Be careful, however, and make sure that the pitch waver is not in the recording itself.  Keith Jarrett recordings on ECM are pretty much guaranteed to not have this problem.  Narrow your choices this way then move on to other sound considerations and be mindful of the inevitable effect of different arm/cartridge combinations.  Pitch stability impacts just about every other aspect of LP sound and is the one aspect that is almost entirely dependent on the turntable regardless of arm and/or cartridge.  Good luck.

One LP that brings many stereos to their collective knees very quickly is Paranoid by Black Sabbath. You'll need the original Vertigo English or German white label (not a promo) pressing in good condition. Most stereos simply can't play it at volume- there is a lot of bass energy in the first track.
Verdi Requiem, side one track two, Soria Series on RCA (dowel spine box set). Vast dynamic range!

Thank You Frogman.  The Koln Concerts is always one of my Go To recordings. Second is a box set of Miles' Prestige years with Coltrane