When I punch the gas (not even all the way) the car almost acts like its going to stall, itll do nothing then jerk forward for a second then nothing and jerk forward again. Whats the problem?

Could be a number of things.
Does the ses light come on when this happens?
How does it idle, can you rev it up fine?
Could be a vacuum hose came off, ignition/spark,....tranny etc.

ses light?

it idles fine

For starters, seperate what the motor is doing vs. what the car is doing.

When you go to full throttle from idle, is the engine accelerating smoothly per the tach in the panel even though the car is moving in fits and starts? (The difference is a transmission problem as opposed to an engine problem.)

Another way to look at this...with the transmission in park, does the engine rev freely? (this is seeing of the engine will accelerate off idle with no load from the transmission on it.)

SES..."Service Engine Soon" or "Check Engine" light in the dash...the computers way of telling you that it thinks a problem exists

it always sounds like the engine is dying kinda. When I drive it normally without punchin the gas it seems to drive just fine.

SES light is the check engine light

We really need more information to help you out. But lets start with some easy stuff. Have you checked your plugs? How about your plug wires? Make sure none are grounded, burnt. make sure plugs are not fouled, dirty, worn out. Once you check these we can move on. If possible, get a picture of the plugs for us to take a look at.

When I bought the car I was told it was given a complete tune up (was told after I paid and everything so I knew he wasnt saying it just to sweeten the deal), it was only bought about 2 weeks ago and has barely been driven at all, maybe a grand total of 50 miles

Ok, if it will accelerate if you roll on the throttle, but stumbles when you snap the throttle open, then (barring any error codes from the computer) I'd start going through the normal maintenance items (cleaning MAF'*, checking plugs and plug wires, going over all the engine vac plumbing looking for a leak.)

What normally happens when you snap the throttle open is the computer (ECM) sees the throttle going open from the TPS sensor, and it should also see the vac dump (MAP sensor) and an increase if MAF sensor readings. It uses that to guess how much fuel the motor is going to need to accelerate as fast as possible (as well as ignition timing changes)

Now...1.) Have you made any changes to the motor or it'* induction system? 2.) Do you have a scan tool available to you so you can see what the computer is seeing from the sensors?

Never trust this. New(used) cars always get all new fluids, plugs, etc right after you get it. Or at the very least checked. Check each system here. Easy stuff first, then we move on. We'll go threw the ignition system first, it'* easy. Then fuel. Fuel filter is a possiblilty but that'* a pain to change. Have you checked for vac leaks? For this take carb cleaner and spray a little bit on the vac lines while the engines running. The idle will change if you spray on a leak.

No and No unfortunatly