I'm going to make an unconventional suggestion- H&R/NEF single shot. Yeah it's not as tacticool as a Vang Comp 870, Benelli M4 or Mossberg 590, but they're inexpensive and very handy as well as light. They do kick though! I've got a H&R Topper in 20ga that I chopped to 18.5", reset the bead and had the barrel threaded for a choke tube and installed Choate furniture on. It breaks down quickly (remove one screw from the forearm), it's short overall (shorter receiver than a pump; use a youth stock), is actually a lot faster shooting than you'd think and with the choke tube in it throws a great pattern. I've actually shot skeet with it just to prove a point as well as shooting rabbits.
Watch Clint Smith (especially at 1:45)
With a little practice you can easily bust more than one clay in flight. The trick is to have a gun with an ejector (the older models) and index an extra shell(s) in your forward hand. be forewarned that the older guns really ejected the shell- as in it really hurts if it pops you in the head. I rotate the gun slightly outward when I break it open so it kicks the shell over my shoulder.
Yes, I'd prefer my 870 if I knew I needed a shotgun* (I've got an early Scattergun technologies conversion/ pre-Wilson) but the H&R is so light and handy that it gets carried on the tractor and four wheeler, tossed in the back of the truck, etc just because it's so handy. That said, I also like the Mossbergs with their extended tubes. I do not like folding stocks on shotguns. Contrary to popular belief you still need to aim, especially with a properly choked gun and quality ammo such as Federal with the flight control wad. If you want a shorter gun, put a youth model stock on it. The greater amount of control, even when hip firing or point/snap shooting, is worth it.
*I'm not a huge fan of the shotgun for most social work; I prefer a carbine.