From your questions you should consider going to a professional.
Are there any check engine lights? If so, go to your local autoparts store and have the DTC codes read. Post the full DTC codes. Note, a flashing check engine light means "misfire".
If you would like to try to fix it yourself, first check for vacuum leaks. Don't cut corners. Even a tiny vacuum leak can cause problems.
Clean the MAF. Use only a cleaner designed for the job.
+1 on the fuel filter.
This could also be an ignition problem. How old are the spark plugs? How about the condition of the spark plug wires?
Try this old racers trick. Run the car in a totally dark location. Look for the blue hue of escaping spark. Look for white spots on the spark plug wires which is evidence of escaping spark. If found, replace the wires.
2003 GT Convertible (sold & missed)
2000 GT coupe (Craigslist project. Fixed. Now my DD). Windsor to Romeo swap.