hatch92_88crx

I just bought an 86 n/a gxl a week ago, and when i take off from a standstill (granny-style, not hot-rodding) the car shakes a bit until i get to about 1600 rpm or so...when in neutral, if the motor is revved there is no such shaking. After the car is moving, yet still in the same relatively low rpm range (i.e. 2nd gear and so on), it won't happen anymore...so it only happens in first gear and reverse. If I am making a turn, it vibrates worse...this makes me think it has something to do with suspension/driveline. Also, the gears grind a bit from time to time, especially on a down-shift....it's nearly impossible to shift to a lower gear if the car is in motion. Any ideas what the case may be? My bet so far is U-joints....has anyone had this type of problem, or has anyone here replaced their U-joints? Thanks in advance,
Russell