Best way to transfer certain files from old iMac to new (have Time Machine)

Hey guys. I'm going to be in the process of moving my data over from my old iMac to a new one. I have been using Time Machine for a while w/ mostly Snow Leopard and Lion on my old iMac so everything is certinaly backed up via those means. However, the new iMac will be on Mountain Lion and it's a fresh clean install that I really don't want to muck up with all the *crap* I've accumulated over the years. So I've decided I only want to transfer the important files to me and I'll install any applications fresh later. The files I really need are my extensive iTunes library, all my photos, all my documents. My e-mail is on IMAP so I believe that will sync on its own.

Can the Time Machine migration assistant that pops up with a new computer at setup able to do these specific tasks without an all or none deal? Or should I copy and paste out of Time Machine or maybe even the external drive itself. I've had issues copying and pasting iTunes libraries in the past where it lost its entire architecture some how.

Any advice appreciated