Having trouble when tring to accelerate in my 2001 Mitsubishi Eclipse GT, what things should I look for?

I have a 2001 Mitsubishi Eclipse GT (3.0L V-6) Manual transmission, the car shifts normally, with no problem. But when at a stop and trying to accelerate the engine revs up and the car very slowly moves forward.. then it will start to catch and accelerate, but still runs at a slightly higher rpm then normal. The RPM's will drop down to normal once I reach speed, but if I try to pass.. I give it gas, it again revs up before it catches. What things can I look for before I take it to a shop.