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I am looking to build or buy upper for plinking but not sure what caliber to choose. I will be for shooting steel
targets and rocks, just an all around fun gun. The range is full of boulders and unlimited ranges. The steel targets start at 200 yrds and got to 1000 yrds.
I reload so I am not limited to caliber. What I want it something that is cheap to shoot/reload in bulk. As this will be for plinking,
it doesn't have to be very accurate, as long as it can hit a manhole size target at varying yardages, I will be happy.

There are so many calibers out there now for the AR its hard to choose just one. Every time I think I have it narrowed down to
what caliber it will be, I find more info on another caliber. The 6x45 looks good but so do the other 6mm and 6.5mm calibers too.
I like the 204 but the 20 Practical and Tactical  look good too. The lack of recoil is a BIG plus!!!

At this point now all I have is a AR lower. Had a 223 and 204 for a very short time and didn't get to even sight them in.
I have a 5.56 AK but it only has iron sights and have not had luck hitting past the 200 yrd steel target. I can hit the 200 yrd
one all day long but not sure if the 223 will make enough noise at 300 yrds to hear it with ear plugs.
Will a 5.56/223 work for me or is there another caliber that will do a better job?

I think the 223 is probably your best bet for an all around plinker. Ammo is still fairly cheap and reloading components are all over the place. I just built a 6x45 16" that I haven't got to try out. I'm just waiting on dies and bullets. The 6x45 is certainly another option for you but the 223 is the cheapest.

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I've heard them out to 500 (75gr fired from 20" barrels).

But for a universal plinking round?  4 come to mind.
.22LR - cheap and probably the world's favorite for 100y and less.  Can't realistically be reloaded.
9mm - inexpensive, reloadable, but 200y (and up) with a 9mm is more like calling in artillery...
5.45x39 - another cheap round (currently) that has some good BCs for those longer range shots.  Cheap to fire, but a PITA to reload (see the 5.45 FAQ).
5.56 - Not as inexpensive as it once was, but it IS reloadable, reloads can be inexpensive.  Lots of load data and options for loading.

IMHO the 5.56 is what you seek.