The best type of stone is the stone that will bake your style of pizza in the right amount of time at the temp you're working with.
Generally speaking, there's sweet spots for baking times for each type of style:
Neapolitan - 45 seconds to 2 minutes
Coal/Neo New York - 2 to 4 minutes
New York Style - 4 to 5 minutes
To break that 5 minute barrier in a home oven that maxes out at 550, you need a highly conductive stone. Firebrick isn't conductive enough, nor is fibrament or unglazed quarry tiles. Cordierite should be, although, I wouldn't use cordierite in anything below 550. For an oven that only goes to 525, you're going to want the most conductive stone available- soapstone. If you happen to be cursed with an even more anemic oven than that (500 or below), you could play around with an iron pan, or, more preferably, you could tweak your oven so it'll go hotter.
Thicker stones have more thermal mass, so they store enough heat to bake an entire pizza (and don't need to be replenished by the burner below, which takes forever) as well as retain heat for ensuing pies. If you're going with soapstone, that means slab soapstone at 1.25", or, if cordierite, a 1" thick kiln shelf. The one downside to thicker stones is that they take longer to heat up, but with conductive stones like soapstone or cordierite, it shouldn't take that much longer than an hour.
One nice thing that I've been noticing about more conductive stones is that you can pre-heat them to lower temps, and, when you put the broiler on at the beginning of the bake, it stays on for a longer time. If, for instance, you have an oven that goes to 550 and you pre-heat the stone to 550, when you set the dial to broiler, it might not even turn on/glow red. The longer you can get the broiler to stay on during that 5 minute bake, the better.
Grilling is a whole different ball game. Most grills don't have that 550 degree ceiling. With the higher heat, you can use something less conductive like firebrick. In fact, sometimes firebrick is preferable because it insulates the bottom of the pie while the heat laps around it and achieves better browning on top.