Generally one should spend about 1/3 or less of the budget on electronics, with 2/3 or so spent on speakers since their quality makes the most difference in what you hear.
The room equalization software available in most modern receivers can make a noticeable improvement in acoustics, though. In your price range, Audyssey is the most popular and is provided by many receiver manufacturers (e.g. Denon, Marantz, NAD, Onkyo, Integra). Anthem's ARC is comparable, but I think their equipment might be more expensive than your budget. The proprietary equalization packages provided by Pioneer (MCACC) and Yamaha (YACC) don't equalize the subwoofer. (Audyssey MultEQ does. Audyssey 2Eq doesn't.) As best I can tell, Harman-Kardon's EzSet/EQ does not do the full-bandwidth equalization done by the other EQ software packages.
I suggest you make a checklist of the other features that you need, like a phono preamp, and use that list to help choose among the options available on the various products. In some cases, an external phono preamp might be preferable to the more limited phono preamps provided in some of the receivers currently on the market.
