welcome to the site George! Show us some pics of your new beauty when you can.
A few things cause the wandering. Bias ply tires (non-radial) can do that, improper front-end alignment is most likely though.
just to be sure so there is no confusion, be aware that these Impalas of the mid-late 60's had a high powered P/S units and the steering box required many turns "lock to lock". (full left to full right)
Your wandering problem sounds like the alignment, not what some others may call loose steering that was made for moms and old ladies to drive these big impalas.
I might add when everything is spot on and tight it will still feel vague compared to a modern car. Chevrolet did that intentionally to isolate you from the road. You where supposed to experience driving as being akin to sitting on your living room sofa and watching the world pass by your big glass window as you cruised effortlessly down the road at 45mph (the top speed these cars were designed to handle back before the age of limited access highways). It wasn't until the mid eighties before you could feel any input back from the steering wheel.
Good news a mid eighties steering gear box bolts onto your frame but you will have to change the hoses ends over to O-ring sealed fittings with an adapter.