NR1402 would be next to worthless with those speakers in my opinion.  If you don't need a home theater receiver, then don't get one.  Look at stereo integrated amplifiers.  NAD, Cambridge Audio, Music Hall, etc.  If you need the AM/FM tuner think about a Harman Kardon HK3490. http://stereos.about.com/od/stereoreceiverreviews/fr/HK3490.htm

I doubt biwiring will offer much difference, just use an appropriate gauge speaker wire for your load and run.

http://www.roger-russell.com/wire/wire.htm#wiretable

Will you be asking a receiver to be doing video processing?  Please describe all that you want to do with your system, including what you will be connecting. Thank You.

You might be able to eliminate an HDMI requirement for the amplifier with an alternative configuration.

I believe your video can remain HDMI from the PS3 to your monitor.  However, the audio signal from the PS3 could come either from its analog outputs directly to an integrated amp or receiver, or (preferably) from the PS3 digital audio output to a DAC which feeds an integrated amp, power amp or receiver. 

A possibility would be a preamp/DAC such as the Emotiva XDA-1 and a power amplifier like the Emotiva UPA-2.  The XDA-1 DAC is likely superior to the DACs in either your computer or PS3.  This package is currently $539 delivered with the Holiday/Clearance Sale.  The XDA-1 has six digital inputs which would accommodate your PC and PS3, and volume control.  Might be a nice solution.  The Emotiva UPA-2 would drive the 685s nicely.  5 year transferable warranty.

http://emotiva.com/xda1.shtm

http://emotiva.com/upa2.shtm

http://www.hometheaterhifi.com/digital-analog-converters/1282-introduction-to-the-emotiva-xda-1-differential-reference-dac-for-the-audiophile.html

http://www.audioholics.com/reviews/amplifiers/emotiva-upa-2-stereo-amplifier

Here is that package used for $400 plus shipping. http://emotivalounge.proboards.com/index.cgi?board=emporium&action=display&thread=21173