AM3 and AM3+ CPUs both work on AM3 and AM3+ sockets. Forward and backwards compatible.
Phenom X4s are quad core Deneb CPUs. Phenom X6 are hexacore Thuban CPUs. Deneb, Thuban, and Bulldozer (FX series) are the name of the architectures, like Sandy Bridge and Ivy Bridge. IMO, Deneb and Thuban are better than Bulldozer for gaming (unless you get a FX-8xxx octocore CPU).
The exception to this is the 960T. It's sold as a X4, but it's actually a X6 with two locked cores. That means it uses the Thuban architecture, which is slightly better than the Deneb architecture.
I think T just indicates that it's not really a Phenom II X4 or something. It doesn't really relate to anything else. A Black Edition CPU is the same as K on Intel, unlocked multiplier. However, unlike Intel Sandy Bridge/Ivy Bridge CPUs, you can overclock locked CPUs.
They're hard to find, but my recommendation would be any Thuban CPU, so a Phenom II X6 or a 960T.