I think Audyssey is a wonderful tool and feature to have. Unless you really, really like a receiver that doesn't have it, I don't see why you wouldn't want to have it.
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I'd say the Integra pre/pro is a very safe bet. Nothing wrong with Denon or Marantz. Besides Audyssey audio processing I'd pay attention to video processing as well. Anything with HQV Silicon Optix will be good. Either the Reon or Realta chips. Gear with Realta seems to increase the price a lot. The Integra uses the Reon chip.
Unless you're constrained for space I'd skip receivers and get separates. Buy the amps once and then upgrade only the pre/pro as needed in the future.