Only the first few models supported PS2 backwards compatibility. All the ones that were released in the last few years do not play PS2 games.
And on the second question, it could really go either way. Obviously if there are any exclusive game series' on the PS2 that you like then that would carry over into the PS3 (Ratchet and Clank, God of War, etc.) Both of the consoles have their advantages and disadvantages and good exclusives, so it's really up to you.
Watch these "Console Wars" videos for some in depth comparisons and info.