Most accurate? I'd think 7.63 Mauser, 7.62 Tok, or 5.7 x28 would be the most accurate. I don't have personal experience with the 5.7, but the other two are accurate enough to score consistently on a rifle clanger at 100 yards out of semi-auto pistols.
Most effective is a little subjective, and would really depend on the gun and the circumstance. An SAA in 45 Colt was government-tested to take a man off a horse at 50 yards, or a horse from under a man at 100. At the other end, various mouse guns were common for government assassinations in the Cold War. Dead is dead, and, circumstantially, neither is more effective than the other. Neither is a great idea for most normal circumstances.
As of right now, I think the CZ75 and its derivatives is the most effective combat pistol in operation today. Even if we were to all agree on that point (and I doubt we would), there's still the argument of caliber. A CZ97 or 75B in 45 ACP for "knockdown" or one of the 9x19 ones for capacity - argue among yourselves. You could also split the difference and go with the 9x21 IMI version, but good luck finding ammo.
Best performing? That's a combination of the two , so there's no real one answer...but now that I think about it, a CZ platform firing the 9 IMI sounds pretty cool.
The platform is pretty accurate, the 9 IMI is a good compromise between the submachine gun-esque cartridges at the "blazing speed and accuracy" end of the spectrum, and the knockdown end of the spectrum.
Practicality is the biggest negative.
NOTABLE MENTIONS:
SIG P210 in 30 Luger Carbine: That typically ranks among the world's most accurate semi-auto pistols. And it is basically a scaled-up MAS 1935 which is typically ranked among the elite of historical combat arms. It is unweildy, that spec ammo is practically unobtainable, and even in 9mm it is not practical.
Tokarev TT-33 or CZ-52 - Plenty of power, good accuracy, but all sorts of limitations