I got my first car

( 1994 Nissan 300ZX N/A ) a few weeks ago. When I bought it, this issue was not occuring. What is happening now is, every time I start the car and take off, the ABS light flashes on the cluster, and my speedometer starts bouncing between 0-20 mph. When I tap on the brakes, everything goes back to normal ( no flashing or bouncing ), and drives good for the remainder of the trip. While the light is flashing, the car operates perfectly fine.
Any and all help is greatly appreciated! Thanks.