For case look into Antec ISK 110, its a small mini itx case, that can hold 2x 2.5 ssd/hdd, not that big either and already comes with PSU. I leave you a video for you see if it fits what you are looking for, Antec ISK 110 Mini ITX Build Part 2: Time Lapse System Build
On the motherboard.... all displayports on Skylake should support 4k @ 60hz, but its going to be tough to get DP + DVI + VGA, most only come with 2 video out, the only that i saw with triple video that have Displayport + DVI + HDMI is ASRock Z170M-ITX/AC
(also has dual Lan, intel and realtek), if you were to accept Displayport and dual HDMI look into ASRock Fatal1ty Gaming Z170 Gaming-ITX/ac
, the rest you either have to sacrifice displayport or accept only 2 video outs.
Now if you were to be fine with Haswell instead of Skylake, some other options open up, that are worth considering,GIGABYTE GA-Q87N
DP + DVI + DVI ASRock Z97E-ITX/ac
DP + DVI + HDMI + HDMIASUS H97I-PLUS
DP + DVI + HDMI + VGAGIGABYTE G1 Gaming GA-Z97N-Gaming 5
DP + DVI + HDMI
Crosshceck the manuals if the DVIs are dual link.