You can use any guitar controller with GH:WT, but the newer guitar comes with the slider frets for the solos. Other than that, it's not a problem.
I'd get Rock Band 2 instead - the tracks are better and there's a huge amount of downloadable content through the PS3 Network. GH:WT only has a few songs so far to download - despite many promises of lots of extra content.
The game will work without the drums and mic, but it's not as fun and you're not getting everything out of the game. Any USB mic will work through so if you have Singstar then those mics will be fine