Well you mentioned the word "Audiophile," You are not going to get audiophile quality with that budget and with wireless speakers. $200 - $350 may get you a decent receiver but most audiophiles would not consider something in that price range audiophile quality. Decent and nice sounding with something like an Onkyo TX8255 - around $200. Any decent receiver is going to have various adjustments which you are referring to as "sound calibration."
Wireless speakers use FM radio signals to send the signal through the air. That's a big compromise and they aren't truly wireless unless they are battery powered - they still have to be plugged into the wall. They also don't need the output power - the amplifiers - of the receiver so you are wasting that feature - you might as well get a pre-amp / tuner instead. Wireless speakers must, as a necessity have built in power amplifiers which usually are not as high quality as the amplifiers in a good quality receiver. It's not difficult to hide those "ugly speaker wires." And good old copper still is still the best way to transmit the amplifier's power to the speakers. They can be run through walls, along baseboards, under carpets etc,. There are even speaker wires made that are flat and designed to be run under carpet and such things. The question of cost comes up here an awful lot. Everyone wants good sound for very little money. It's just not possible unless you want to build speakers and purchase used gear. That's what I did for the most part. Still, the smallest system I have (in our bedroom) probably cost me around $650 - $750 for the receiver, DVD player, VCR and the various speakers that I built / rebuilt. I wouldn't consider it hard core audiophile quality but it is by far, head and shoulders better than any of the "all in one" HTIB (Home Theater In a Box) systems. And that is what you want to avoid - HTIB systems. They reek of cheap, junkyness and when one part malfunctions you are stuck with a bunch of other parts that can't be used with anything else. IMHO the best thing you can do is get a good but inexpensive receiver and a similar set of wired speakers. Preferably speakers from a company that specializes in speakers and doesn't make a million different electronic gadgets as Sony and Bose do.