tonearm parameters

I've been reviewing turntable recommendations, on this and other forums, and what I'm struck with is advice that often you should upgrade the tonearm. This is especially true of vintage Thorens, Technics ,Luxman,and many other turntables Frequently, [not exclusively] Rega tonearms are recommended. We'll, I've had Rega P3,P5,RP6, and currently, RP8 turntables as well as Music Halls and Project TTs. In addition, I've had VPI TT's. I'm at a loss as to what is optimal in Tonearm qualities, and respectfully request from Audiogon members what exactly are the paramaters to look for.