I don't know much about the A300. As for the 870, I own one that I bought about 5 years ago, cheap finish and cheap wood. I think Remington has cut production standards on these guns, so I'd be careful (I always liked Rems, owned a couple older ones, and bought two in the last 5 years or so; not happy with either one). Maybe the Wingmaster line would be ok, but I'm not so sure about the Express line. I also own a Benelli Supernova, which would fit within your budget. If you're not dead set on an autoloader, check one out. If I were you, I'd get some guns in mind and go down to a gun shop and see how they feel.
Also, I'd look at a 26 inch barrel for an all-purpose gun. It's kind of a compromise. Generally, you want shorter for turkey, longer for waterfowl, so go in the middle.