If the steering gear is like you describe it will need to be removed & rebuilt. The kit will contain brgs, bushings & seals but if its as bad as you describe there is probably a lot of wear in the gears. If you tear it down & find that it might be better to find a used one to start with. They are not too hard to rebuild.
Like otto says raise the front end & shake it down. There should be no play in any of the joints like the tie rod ends & drag link. Grap the wheels at 12 &6 o'clock & check for play in the king pins & wheel brgs. Grease all the fittings & make sure grease flows through the king pins. Often sticking king pins are the cause of road wonder.
A small amount of play in the tie rod & drag link ends can be adjusted if it still has the old original ends. A lot of play in them will call for replace ment.
George