My PA28-181starts OK if the manual is followed, but I've seen some epic fails by others trying to get it started especislly when hot.
When hot no one seems to like the idea of the mixture being in the lean cut off position.
It seems to be a need thrre hands situation. Seems mixture in lean cut off, throttle half inch open as opposed to the usual quarter following a couple of throttle pumps, crank it and when it catches smartly xture to full rich - works every time from cold, same deal but full rich, quarter inch and three or four throttle pumps - can prime instead but the Essex primer lock is fiddly.
The engine is a Lyc 360-A4M - must admit this is in the Caribbean so it's never "UK cold"