I worked at a range for several years that rented and sold class III toys. We had an Uzi, MP5A2, MP5K, M11 .380, S&W 76 that were shot a lot and a few Mini 14 / AR15 Conversions that were shot very little.
The two that I liked best were the Uzi and the M11 .380. Both are very simple designs and easy to maintain. Our MP5s were much more difficult to keep clean and took a lot more cleaning to keep working day after day on the range, but were more accurate, and had better ergornomics.
The M11 was the most fun, simply because if fired roughly 1600 rounds per minute and was a hose. Nobody could get less than 6 or 7 round bursts out of it. Very hard to control without the stock and barrel extension, but it sure was pure hell out to 25 - 30 feet. Most fun of the bunch hands down in my opinion, but VERY hard to control if shot as pistol full auto.
The S&W 76 was ok, also very reliable and simple, but I didn't like the stock and the entire gun would heat up too much to be comfortable to shoot if you put more than a couple of mags through it in a a hurry.
The UZI would be the one that I would most likely buy if I ever decided that it was worth the ATF hassle. Ours fired pretty slow, around 500 rounds per minute, and was very easy to shoot accurately full auto. It was quite a bit more controllable than the Thompsons that we ordered for customers and got to fire upon occasion. Also, at 500 rpm it is pretty easy to squeeze off just one or two shots at a time with a little practice. There are also a couple of different wood stocks out there that make it more comfortable to shoot still.
I would tend to stick with pistol caliber weapons, simply because they are generally cheaper to shoot, quieter, and can be fired on a lot of ranges where .223 or 7.62x39 can't be. The rifle calibers are much harder to control for most people when they are just starting out, and our rifle range had all of the walls, ceiling, target hangers and lights constantly shot up by people with the converted Mini and ARs, not to mention the occasional AK that someone would bring in.
Also, if you have never been around when a ~10" barreled AR carbine is fired full auto with cheap Win USA .223 ammo, you are missing out on a monster of a fireworks display!!!
A fun but less hassle option if you are not familiar with them, look into some of the Airsoft guns. Try 747 Imports on the web to get an idea. They are electric powered plastic bb guns that are the same size and shape as the original guns, roughly the same cyclic rate, and you can shoot them in the yard or house without getting the neighbors and the feds all worked up. 80% of the fun of the original, especially if you get the traser unit and shoot the GID bb, so you can light up your low light shooting with elegant bright green dots arcing across the field of fire.
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