One small thing to keep in mind.. If you do consider buying a late 30's Bendix machine, they didn't have any suspension, so you had to bolt them to the floor.
One common issue I've noted here is that a lot of people find these machines with seized timers. There are a lot of timer rebuild shops which can repair them.
The Bendixes shown in the pictures above are the Deluxe (Square) and Standard (Round) model. Both are pretty much the same machine, just one is tarted up a bit. The Deluxe model I believe is the more highly sought after one. (At least from a stylistic point of view, but that's purely personal taste.)
The Bendix machines only had a 200 RPM spin, which is about the same as a wringer. If you were going to consider buying one of these machines, I'd recommend purchasing a separate clothes spinner to get the extra water out.
The 1950's were certainly a golden age when it came to automatics, but I think the most stylistic and glamourous machines were from the very late 1950's, early 60's. Especially around the 1956-1963 era.
I could suggest a multitude of vintage machines all day long, but I'm afraid I might cause a flamewar by mentioning one brand over another.
If I was going to consider buying a vintage machine myself, here's what my own personal preferences would be:
Whirlpool - 1957 Imperial.
Frigidaire - 1960 TOL (Custom Imperial I think)
Kelvinator - 1955.. maybe '56?
Philco - The 1959 "Automagic"
GE - 1960-1962 TOL Filter Flo .. Or the very rare 1967 Versatronic machines.
Maytag - 1970's vintage all pushbutton A902
Bendix - 1958 Duomatic
Hotpoint - 1961 Touch Command
Westinghouse - Either a 1958 Laundromat or a 1974 Heavy Duty 18 with Weight to Save
Norge - 1958 Dispens-o-mat
Kenmore - Perhaps the 1950's (Don't know exact year) "Frogeye" machines.
Easy - The Combomatic! (late 50's?)
For twin tubs, they're less desirable to me and not automatics, buuuuut...
Hoover - Any hoover made with a "Boiling Action" impeller.
Maytag - Maytag made a dual impeller twin tub, this would be just as suitable.
Easy - The easy spindrier - Another option. Preferably a pre-war vintage one.
I'm not really big on conventional wringer washers.
I wish you the best of luck on your search!