Play in the steering is usually caused by worn tie rod ends or idler/pittman arm. Grab the tire at 9 and 3 and shake side to side to see where your movement is. Bearings will have play in that direction and when grabbed at 12 and 6.

Shouldnt need solvent to repack the bearings, some brake parts cleaner and a box of blue shop towels will get most of the old grease and crud out. Place a small dab of grease in your palm, and force it between the rollers on the bearing. Be sure the inner seal isn't trashed and it goes in straight. Going to need a torque wrench to properly set the preload on the bearings so they don't burn up or have too much movement.