Power - where to start? Mains, chords, conditioner, filter?

For all the nay sayers of upgrading cables, using power re-generators, and dedicated power circuits, think the process through. ALL AC voltages have noise and harmonics, which gets induced to any electrical component near by. So buying high quality cables which shield the radiation of this noise will help reduce the overall noise floor of the surrounding components. Re-generators take the power and completely remakes it to a pure sine wave  60Hz 120 VAC for the U.S.. Using dedicated power circuits removes all the possible external devices such as fans, transformers, and all the other crap we have plugged into our households, however due to the common neutral ground configuration this is only a minor improvement overall. 

Also, I would great suggest using a power regenerator, taking your house AC and completely "regenerating" and removing all the harmonics and noise in it. 
I have used a PS Audio re-generator, which made incredible improvement "removing" noise, it didn't change the sound, it made the sound cleaner and have more clarity. I also replaced all my power cables with well made high shielding AC cables to block any noise that each component might generate from their power supplies. 

These 2 upgrades made significant improvements in the clarity of my music and enjoyment. 

I just hooked up a Transparent PowerWave (power conditioning system).  I've a Linn DSM Selekt and Wilson Sophia 3 speakers.  This combo sounds great.  But I was blown away with the improvement in sound quality with the PowerWave.  You can more clearly hear different instruments and the sound stage is deeper and more realistic.  I'm hearing things in my favorite songs that I've never heard before.  All the power cords are stock, except for the Linn which is using a Nordost power cable with.  I'd see if one of your local HiFi shops will let you demo a good power conditioning system at home so you can hear for yourself the difference they can make. 

I recommend running a fresh dedicated 20 amp line from your main circuit box to the location of your system. Use Hubble hospital duplex devices. Use of power conditioner is optional as needed.

I also live in an apartment and greatly lowered my AC noise floor by powering all my gear from a balanced AC power supply from Equitech, the industry leader .
 Modifying the wiring and plugs in my place were not options without risking eviction .I did later make my own power cords using Oyaide's Black Mamba cables and gold plated copper plugs and iec connectors to great benefit .

A side benefit was that the colors on my television also became richer , with blacker blacks . YMMV

In my opinion, the place to begin is with one or better yet two dedicated circuits with 20 amp breakers and wire runs of 10 gauge although 12 gauge would work. In addition to that use high-quality AC outlets.

Agree completely and that's exactly what I did when I set up my current main system (I located the system in the next room to the main panel).

I use a filter (Inouye - http://inouye.ca/index.php?page=Products) on all front end source equipment (sources, phono preamp, preamp), which makes an obvious improvement, but not on the power amps, which suck too much to go through most power conditioners.