Rick, the uppers in the calibers you mentioned interchange between AR-15 recievers without any problems, some Colts require an adaptor pin due to a different size hole in the front of the reciever, the newer Colts use the standard M-16 size front hole as do all the other lower manufacturers that I am aware of. If you wish to use pistol caliber uppers there are some slight modifications that must be made, usually different buffer/buffer spring and a different hammer and some type of mag well adaptor. The 7.62X39 and the 6.8 will require different magazines but I imagine you already knew that. Also you can not legally put a pistol length barrel (less than 16") on a rifle reciever (with or without a stock) without first registering the rifle as a short barreled rifle with the BATFE. Now you can have an AR pistol (unless local laws prohibit it) but it must be on a pistol reciever. The only difference between a pistol and rifle reciever is how it is designated by the manufacturer. Yea, I know that is confusing but that is the way the law is.
Now to interchange between the 308, 243, WSM family of cartridges etc, you must use an "AR-10" reciever and there is a lot more variablility in those, to my knowledge the Armalite family and the DPMS family of uppers will only interchange with the parent companies lowers but this may not be correct. Your best bet on this would be to call the respective manufacturers of these rifles and talk with them about it also they are quite a bit more expensive than the AR-15 family of rifles
The AR is a very user friendly platform and in the 5.56 version with a correctly assembled rifle is accurate and reliable. A lot of the bad press the AR gets from reliablility is from the early M-16s which as I understand it had some issues. The ARs work great as long as they have good magazines and good ammunition. I don't know about the 7.62X39 or the 6.8 I have not shot the 7.62X39 enough out of an AR to have an opinion about reliablity or accuracy and I have not shot the 6.8 at all. But it does make sense to have one or two lowers and several uppers but what usually happens is that you start out this way and then build or buy lowers for the rest of your uppers but either way you will probably enjoy the rifles.
One last thing, stay away from the cast lower recievers. All of the ones that I have dealt with have had tolerance issues and while this is aggravating if it is a single rifle, would be maddening if you are trying to switch back and forth between uppers. Go with a forged lower from a quailty source and you will prevent a lot of aggravation.