1990 golf sputtering and dying

[Brickman2929]

When at lights the car hesitates and then goes normal once it accelerates. it died the other day for the second time while going 50km down the road. While waiting for a tow (1 hour) we tried it again but it would not catch. i decided to push it off the road and my wife instead of turning the wheel she turned the ignition and it started up ???????? Why would this happen?
Now i am really nervous to drive it anywhere. What should i check under the hood???