I have a 1999 Hyundai Accent 1.5L Base model with a manual transmission. While you are driving down the road, the front end will randomly jerk to the left and then sometimes back to the right, almost like it is floating, but with a hard pull on the steering in either direction. The tires are good and for the most part has a good alignment. I can't figure out what it could be because it is not just pulling to one side.

These are the times when it happens:

Clutch is engaged to shift gears at normal highway speeds
During acceleration at normal highway speeds

NOT during braking or when the accelerator is held at one constant position

It has manual steering, not power. Does anyone have any ideas? Rack and pinion or A Frame maybe? Would like to fix it myself, but not sure where to start or how much I am looking at for parts.