I'm a Pentax shooter and can comment on the LX. It is a wonderful camera, excellent ergonomics, (for me!) especially with the Grip B added. Very smooth acting wind, metering (center weighted) is very accurate and consistent. Auto exposure from about EV -6 to +20. As someone above commented auto exposures can run to many, many minutes. Since the meter reads off the film changes in lighting are compensated for, and there's no need for a viewfinder blind. The camera is weather sealed, although after so many years that may not be dependable.
Ideally you could handle examples of the three you mention. A camera is ideally a very personal possession, I'm sure many of us have bought a camera and never "warmed" to it. For example, the Pentax is quite small for a professional system camera, this may be a factor in your decision. I've found that the winder, which is not too hard to find, adds a little heft which is nice, and also furnishes power rewind. Pretty cool!
Now as with any camera there are downsides. Any old camera probably needs a professional CLA; I'm not sure Pentax is still servicing the LX. Eric Hendrickson in Tennessee is the Pentax expert, his charges are moderate, but the LX is intrinsically expensive to work on, especially if the integrity of the body seals is preserved. Beware the "sticky mirror" syndrome, in which the mirror action is very slow, or the mirror refuses to descend. A proper CLA would run about $150. As with any old camera be sure you can return it in case there's a problem. With the LX make sure the speeds below X sync work; they are electronically controlled and thus vulnerable. If it will furnish a timed proper exposure of, say, five minutes, it should be okay. BTW, X sync is only about 1/70 sec, pretty slow by today's standards. So it goes with a horizontally run titanium foil shutter, I suppose.
An operating LX in reasonable condition would cost probably $350 to $400.
While the LX can use hundreds of lenses, back to the first K mount, Pentax label lenses aren't as commonly available as, for example, Canon or Nikon. While the LX is a full system camera, finding a motor drive or a 250 exposure back for the LX is not easy, nor is finding the various system viewfinders, nor the interchangeable screens. BTW, while Ricoh uses a variant of the K mount it has an extra pin which can "lock" the lens onto the mount of a Pentax digital SLR. I don't know whether this applies to the LX. Like the Hassie the LX uses special lugs for the neck strap, if your purchase doesn't come with them there is a strap with compatible ends from B&H or Adorama. Not as attractive, however.
I also have a Pentax 645n, like Alan Gales says its like shooting with a big, noisy 35mm SLR. I'd suggest the 645n, which has a better viewfinder than the original 645, autofocus with confirmation beep/icon, film edge exposure imprinting, 16 exp per roll rather than 15, and a really intuitive operation. Wonderful lenses, but no third party producers. Note that the longest reasonably priced tele is 200mm, about like a 135mm on a 35mm camera. With a hard to find adaptor the 645 can use lenses from the Pentax 67, but that camera's long lenses are pretty costly. It uses inserts, so no mid-roll switching. BTW, the 220 inserts are usually cheaper than the 120 and are easily "converted" to 120 with a tiny screwdriver and a little care.
Ken Rockwell, so often dismissed, has a good "take" on the 645n and a few of its lenses.