My car is stalling.

I have a toyota avalon 97 which has 177000 miles and recently it started having problem with starting. Sometimes it starts well without any problem and sometimes it refuses to start until after many trials. Recently i stopped at the stop light and when i stepped on gas it started stalling (it wanted to switch off on me) i realesed gas pedal and step on it and it went on well. another day i was going at 45 miles per h and at this time it kind of shook alittle bit and the trac off light came on together with the check engine light. I took to auto zone and the code was p0420 so i dont know if the cat which is bad or the fuel filter. Please i would appreciate for your help