Recommendations on cooling and case for a 6700K/1080/TB3/2xM.2 build

Since choosing a case is completely a personal choice, it's hard for us to suggest which case to go for. That being said, i'll tell what i would do (based on my preference).

1. Ease of building the system
The ease of a build is mostly depending on the experience of building a system rather than the case used. For example, cable management is a nice headache, regardless the case used. Still, bigger cases (e.g full-tower ATX) offer more room to work in than smaller cases (e.g micro ATX).
Here i suggest Corsair 760T full-tower ATX case,
specs: http://www.corsair.com/en/graphite-series-760t-full-tower-windowed-case
(Same case is used in my Skylake build, specs in my sig.)

2. Minimum number of cooling components/simpler cooling components/smaller cooling components
Less fans usually means lower cooling performance and i don't advise using only 1 or 2 case fans.
Regular case fan is the most simplistic cooling component there is.
To move the same amount of air, smaller fan means higher RPM than bigger fan and thus, more noise. For example, to get 50CFM, 80mm fan spins at 2000 RPM while 140mm fan spins at 800 RPM.

3. Low Weight
That implies that you're planning to move your case a lot. If so, get a case that is designed for easy moving. E.g Corsair Vengeance C70.
specs: http://www.corsair.com/en/vengeance-c70-mid-tower-gaming-case-gunmetal-black

4. Low Noise (I'm assuming I can get a reasonably-quiet system without having to make trade offs with 1-3 above, but let me know if otherwise)
Low noise is depending on the fans you use. Fluid dynamic bearing fans (e.g Arctic Cooling F series) or magnetic levitation bearing fans (Corsair ML series) are the quietest. Also, bigger fans with lower RPM also help to reduce the noise (explained that in 2nd point).

5. Smaller Case Size (but not at the expense of any of the above)
For smaller case, a mid-tower ATX is standard option. Here i suggest beginner friendly Corsair Carbide 270R,
specs: http://www.corsair.com/en/carbide-series-270r-windowed-atx-mid-tower-case

6. Transparent case with LEDs that change dynamically based on temperature (but not at the expense of any of the above)
For transparency, i'd suggest Corsair Crystal 460X case.
specs: http://www.corsair.com/en/crystal-series-460x-rgb-compact-atx-mid-tower-case

The eyecandy with LEDs can be easily achieved when using NZXT HUE+. If you also want fan LEDs to adjust according to the case temps, use NZXT Aer RGB fans.
HUE+ specs: https://www.nzxt.com/product-overview/hue-plus-features
Aer RGB specs: https://www.nzxt.com/product-overview/aer-rgb-features

7. Ease of cleaning (e.g. removable dust filter or equivalent)
Quite a few cases come with some stock filters. Usually those filters aren't good enough. (Just like Intel's stock CPU cooler isn't good enough and a lot of people are buying aftermarket coolers instead.) Using an aftermarket filter set will help.
I use Demciflex filter set on my Corsair 760T case. The aftermarket filter set keeps my system clear from dust and cleaning the filters are very easy.
Demciflex site: http://www.demcifilter.com/

For eyecandy, best setup would be Corsair Crystal 460X, NZXT HUE+ and NZXT Aer RGB.
For moving, best would be Corsair Vengeance C70.
For ease of the build and cleaning, best would be Corsair 760T with Demciflex filter kit.

You can also use NZXT HUE+ and NZXT Aer RGB in the Corsair 760T build for eyecandy. Only downsides are the weight of the PC and size.
(I'm planning to get NZXT HUE+ and Corsair ML140 red LED for the eyecandy to my Skylake build.)