Need Steering rebuild or just old car

I'm not experienced driving old cars, so I have no frame of reference.

My 68 barracuda sort of needs constant adjustment when driving down the road. If I go over bumps, steering can shift, enough that I'm nervous going over 35mph or so in anticipation of some bump.

I've put new control arms, new steering arms/bushings, ball joints and shocks in.
I certainly need an alignment. I haven't yet adjusted the gear shaft either (tomorrow!).

I've also been reading about refurbishing the (power) steering box, or even replacing it with a new design that will give it a more "modern" feel. Before I go dropping coin on either of those, is the alignment/gear shaft adjustment likely to fix the issue if it even is one?

I don't mind somewhat unresponsive steering, so long as the car didn't wander off in directions I wasn't expecting.