Steering must be tight. Correct any looseness. Have someone turn the steering wheel back and forth while you observe the steering action.
Check the balance of the front tires by jacking up the front end and loosening up the brakes and bearings. (Record the clicks of the brakes so that they can be set back to the proper adjustment and record how many cotter positions the bearing nut is moved. Half a turn should be sufficient.) Rotate the tire and let it coast to a stop. Do this a few times and if it always stops at the same position, add stick-on lead balance weights at the top until it stops at random places.
Return the brake adjustments to the original position. Return the nut to the original position and check to see that there is no noticeable play in the bearing. If there is then tighten it one cotter position at a time until any play is gone. Most people tighten the nut until there is some drag on the bearing and then loosen it up one cotter key position. Mark the drum and wheel on each side so that the wheel will be replaced in the exact position if it is removed. (The brake drum is not balanced so that the drum, tire, and wheel have to be balanced as a set.)
An unbalanced tire/wheel will have a natural frequency (rpm) at about 20 miles per hour where the unbalance will be felt the most. At lower and higher speeds the unbalance will be felt less.
The steering must also be aligned properly. Check the tow-in and caster. The tow-in is adjustable but the caster is not. There should be 1/16 to 3/32 inch tow-in at the tire tread.
Check the shocks. Jump on the fender. The car should not bounce when you do this. Adjust the shocks or replace them if needed.