Q: miss fire/fuel issue?

Car in ditch wouldn't start I tried 6x, it was almost on empty so I assume the gas was not getting to the fuel pump, when I pulled car out it started right up drove fine. Next day I get a little stutter/hiccups at low rpm at stop sign, give it gas it dies and when started again is huffin and puffin briefly and dies. Wait 10 min. it starts up drives stutters a couple times and it's good for rest of day. It doesn't do this every time I drive, maybe 3 times in the last week, check engine came on after incident and are po460- fuel sensor malfunction circuit AND po304-missfire cylinder 4. I don't have tons of money so I can't go start buying parts to see if it works. My guesses are (since the attempting to start over and over with no fuel started all this) that it needs a new fuel pump or filter. My research is showing it could also be a number of things, sparks, coils l, cables, pump relay, vapor lock, evaporative leak... do you have any ideas, based on the incident that caused this?

My car has 108000 miles.
My car has a manual transmission.