I Can Think....
....Of two sets of vintage machines that are on a level with your car collection:
One would be a pair of Maytag 906's, a top-of-the-line, all-pushbutton pair made from 1966 to, I believe, 1972. They were extremely well-made, but as daily drivers, may leave something to be desired for some people - all the cycles were controlled strictly by pre-programmed pushbutton, with no options. You either wanted to wash, say, your woolens in the way Maytag provided, or you did not - there was no way to change any of the wash, motor speed, rinse or soak options for any given cycle. They were, however, luxury machines, for people who wanted to feel their clothes were getting the best possible care while making the fewest possible decisions.
Look up "Maytag 906" using the Super Searchalator; you'll see a photo of Fred Nelson's beautimous 906 pair. Fred uses them as drivers.
The other pair you might really enjoy would be a pair of 1966 Lady Kenmores, which have more to recommend them to the person who likes to play with options. They're controlled by both pushbuttons and a cycle dial, with the dial capable of modifying the cycles. There are tons of possible combinations. They are extremely luxurious machines, surprisingly often seen in wealthy homes where no other Sears merchandise was to be found - they had a reputation second to none.
You should know that Maytags are simply and robustly engineered; you can rebuild one with relative ease and have it last for decades. Parts are reasonably available.
The Lady Kenmores are more of a connoisseur's machine, in that they're much more complex than Maytags, with many parts no longer easy to find. It's not that they can't be restored, nor that they can't be used as drivers - people do restore them and use them. But they are often more demanding than Maytags, especially when their detergent/additive dispensers go wonky and need repair (Maytags have much simpler systems for that purpose, and they have almost zero tendency to go out of whack). Super Searchalating on "Lady Kenmore" will turn up some photos.
Maytag 806's are a good balance between these two extremes - you get Maytag reliability, and flexibility approaching that of the Lady Kenmores, without the Kenmores' complexity. Again, search and ye shall find pics.