Good points listed above however not all concern 'floating'. Prior to the downsizing of cars after the '70s fuel crunch most all American cars wallowed. The bigger and the older they were the more they drove like a round bottom boat. Taller, higher center of gravity, bodies set much wider than tire track all contribute to the effect. The older the vehicle, the slower they were driven as there weren't many roads that could support extended high speeds. One hundred horsepower cars with near 4:1 rear axles and no overdrive were never meant to be driven over 50-60 mph.
I think defining the terms I've seen here might be the first step in helping:
Floating - car feels disconnected from the road. Lots of body movement, especially when cresting a hill at speed. Feels like riding on a balloon. Soft springs, light and/or worn out shocks, under-inflated tires, worn suspension and body bushings are primary causes.
Wandering - constantly making steering corrections, difficult to stay in the center of your lane. Loose/worn steering linkage, worn steering gear, low to negative caster setting, under-inflated tires.
Creeping - some tires, especially belted and bias-belted tires, tend to suddenly pull the car to one side as they cross ridges and/or lanes. Sometimes a specific tire line/size will do this no matter what vehicle it is mounted on, sometimes it's a specific tire on a specific vehicle. Even some radials can do this. Best bet is to buy tires that have a center rib, e.g. a tire with five ribs has a center rib, a tire with four ribs doesn't.
Pitching, rolling, porpoising, etc. - hitting the brakes makes the car pitch forward, nose-diving. Cornering, especially at higher speed and quick steering input makes the car feel as though it may roll over on its side. Porpoising is a constant pitching back and forth, most noticed at the end of a hard stop. Also a car that's front end continuously bobs up and down while driving on smooth roads. Again, soft springs and shocks, old car high center of gravity, little or no anti-roll bar(s) (colloquially, and incorrectly, called sway bars or anti-sway bars.)
Radial vs. belted/bias belted tires: The old belted tires (kinda hard to come by these days) didn't cause floating, unless they were under-inflated. They just didn't have much grip and were downright dangerous in rain and snow. Upside is they are a lot easier to steer without power steering, goes along with their minimal road grip. Radials will wallow a lot more than belteds when under-inflated due to their ballooning sidewalls and increased slip angles.
The old Bendix power assist steering will add some steering play when there is no hydraulic pressure present - about 1/4"-3/8" at the linkage. But this only affects wander, creeping and increased steering play, not wallowing.
Alignment settings -
Caster - the more positive the setting, the more the wheels want to remain centered and the more stable the car feels. However it comes with a price. The more positive caster is the more difficult it is to steer away from center. And too much caster can cause some dangerous situations. Ask an old Chevy pickup truck owner if they've ever experienced 'death wobble'. Low to negative caster results in easier, lighter steering but at the expense of straight line stability and return to center after making a turn. Think of pushing a shopping cart backward and letting go.
Toe - Toe is the #1 cause of tire wear. 1/4" too much/little can shred the edges of both front tires in a short time. Notice I said 'both'. Toe affects both front tires equally, you can't have one tire toed in/out and the other not. They split the setting equally. So if you have edge wear on only one front tire the toe setting isn't the problem. Toe is rarely set at -0- because all tires drag to a certain extent. As the tires drag they will pull to their respective side of the car. If the toe was set at -0- they would open to a toe-out setting while driven and chew off the inside edge of the tires (the leading edge of the tire will be the edge to wear.) Too much toe in wears the outer edges. Typically a rear drive car's front toe setting is 1/16" in for radials, 1/8" in for belted tires and more for wider tires (the wider they are, the more they drag.) Front wheel drive is another story. As power is applied the wheels tend to 'pull' to the inside, creating a toe-in situation. However, what was once rule of thumb and setting front wheel drive toe out to compensate doesn't always play these days. Advances in suspension and tires, etc. have some fwd cars at -0- to a small amount of toe in. Now, for the big finale... toe in/out is rarely noticed by the typical driver. Obviously if it is way, way off it will be noticed as 'the car just doesn't drive right' as it affects various suspension designs differently. I've seen cars with drastic toe problems shred their edges to the cord in less than 500 miles. Loose front end parts will 99% of the time result in toe out and the inside edges worn.
Yeah, this is a long post. I just wanted to help and clear up some terms. There is no reason to be afraid of driving your old car at speed provided it is maintained properly. If you don't feel that it's safe take it to someone with experience. That doesn't mean the kids at the tire store down the street. They know how to set an alignment the way the machine shows them and that's about it. Even at that, the alignment machine's catalog of specs probably only goes back to the late '90s. You need to find a geezer mechanic, a spring shop or a hot rod shop with a good reputation to really make old iron drive right.