Not familiar myself with those but I would assume that parts will be hard to find. Little to no reproduction parts so things like interior, taillights etc will be NOS or used IF you can find them. Even the folks with the 60's wagons have a hard time finding parts. All this being said, I love wagons!!!!! Post up some pictures after you go take a look at it!

You can get stuff like tail light lenses for it easy enough. Galvin's has most anything you'd need (www.ramblerparts.com).  
There are no specific things to look for. Just check the "frame" rails for anything more than surface rust. In something this old I don't worry a lot over floors, as long as they are mostly there just fiberglass over on hte inside and undercoat good. Check the cowl for rust -- pour some water in the cowl vents and see if any goes inside. Not hard to fix that either though -- the vent panel comes off.  
 
You will have to make motor mounts for it. The crossmember on the 56-61 is sturdy enough to carry the motor, so you can weld to the existing crossmember. You might want to use something like the Bulltear mounts and a universal hot-rod tubular crossmember. Front rails are 31.5" apart (inside to inside). Something like this: http://www.speedwaymotors.com/S-B-B-B-or-90-Degree-V6-Chevy-Crossmember-Mount,32 73.html. I used one of these to help a guy put a Chevy in an old Rambler. We made 1/8" thick steel pieces for the end bent in an "L" shape to fit inside the stock rails with the short leg of the "L" on top of the rail. Two bolts from the top through the rail on each side held it in. Was a long time ago -- I'm pretty sure that's how we bolted it in... They don't make on for an AMC engine, so the mounts will have to be modified to fit. I'd try the Chevy mounts and make new side plates to fit them to the AMc engine.

It can happen, but it's not "common". Common as in it happened on occasion yes. You know how things like this are -- happens once or twice in a neighborhood and all are bad! That suspension was used starting in 1950, so it had nine years for a few problems to become "common". It was even used on the big Nash and Hudson cars, and the lower suspension remained the same through 1961 on big cars, 63 on Americans.  It needs to be inspected, and preferably disassembled, cleaned, and put back together with anti-seize and modern grease.
 
As for putting in a modern engine, well, there could be problems. For starters there is the fact that all 56-66 big Ramblers use torque-tube drive. So you need to change the rear axle and suspension. Most of the time. There are some exceptions. In a few cases you can use the original transmission, which has the torque tube mount made onto it. A bracket can be made that will hold the front end of the tube to the body, but I don't particularly like that arrangement. It's just a preference -- nothing wrong with it if done well. The V-8 trans can be mated to a newer V-8 (or even a 72+ six) with some careful parts selection, but the parts may be hard to track down. The six cylinder trans is marginal, but will bolt up to a pre 72 six. For a cruiser it will be fine. The 56-66 V-8 trannys are all strong enough for newer engines. The V-8 auto is the BW M-8, very similar to an M-11 as far as strength. No performance parts, but for a mid level engine (around 400 hp or so) it's plenty strong.  
 
The crossmember can't be changed. The pre 63 big cars use a four point mounting system with two mounts near the front and two on the bell housing. The suspension crossmember is, however, strong enough to support an engine. So you can remove the original engine mount crossmembers (I'd leave the front one in for a stiffer structure though) and weld "perches" to mount the engine on the suspension crossmember and fabricate a trans crossmember (or use a universal one modded to fit). I've seen one or two with mounts made to bolt to the engine and use the original V-8 mounts. Naturally V-8 and six mounts are different.
 
 I can elaborate if needed, what are your plans for the car, and what kind of fabrication can you do?

TOM:   I KNOW THIS CAR MIGHT BE DEAD!   But incase you find another wagon, one area thats overlooked is the frame sill thats over the A-arm or behind the  front coil springs they rust out and you can only tell by viewing from under car or peeking behind front tire.
 Also I had done this 401/727 swap into a 62 Rambler Classic 17 years ago, then retired last year and sold it to move on to other AMC stuff.
 I still have a EXTRA rear end  that enables you to rid the close driveshaft it has the hardware welded  and  only needs your choice of gears. $150 firm
 Plus I have  NOS 1/4 panel for  a  59 Wagon left side and a right side for the 59 sedan , both for $150  no shipg.. call for details in case  you pursue  this type swap  502-964-4328