2003 Hyundai Elantra Startup

I have a 2003 elanTra with 128000 miles. It turns over easily but there is a hesitation and rumble once it starts firing...like it wants to stall. However once this passes it runs fine. Once the tachometer spiked up to a little over 2000 rims once this passed. Like I said, runs fine after scary startup. It is most noticeable after the car has been sitting at least a few hours.