How does the car idle once it's not choking anymore? If the idle is smooth at that time, it's unlikely that timing is causing it. Use a timing light to check the timing. If timing is within specification, the belt is installed properly and things are aligned.

It sounds like a combination of weak spark and fuel problems. Does the car smoke at all while it's choking? Does it smell like fuel is coming out of the exhaust? Does the engine run better if you rev it up? Is the ECU flashing any codes? These are all things to check to help narrow down the problem.