So prince was also my first heroic and he wiped me many times. One tip on him with a fresh team if you have shammys is to line them up back in the corridor before Prince's room, all against the wall. Then run in and pull him back to the corridor, then pop fire elementals, they will help a lot with the spawns.
This tip was posted here a while back and works really great if you are struggling gear wise.
Other than this, keep the tombs off your team and nuke him down asap.
For me I actually skipped him on my first team (2 warlocks, hunter and resto druid with DK tank) until I could nuke him (I also switch DK for Pally), my current team with shammies, druid tank and disc priest never had a problem with him.
I think the overall best advice though is not to try to gear the whole team at the same time in heroics, I got my tank geared first, took a couple of days doing randoms with pugs, pretty much instant grps. Then I geared the rest of the team, having a geared tank makes a HUGE difference.