94 Toyota Tercel died, started up later, ran, started dying at stops & wouldn't start unless pushed by a car?

The oil was a couple quarts low and the water got low and it got a little hot as the days got hotter, but I think it's probably something else. My dad filled the oil & water and it worked ok until it got warm then started dying at lights and stop signs, it would start the first couple then it stopped starting and Dad had to push me in his car and it jump started, it's a 4 speed manual. Dad thought maybe a fuel filter? He's no mechanic though, any thoughts?