I'm going to build a new rig, it's gonna be something like a media center. I would like to have a machine that looks like DVD player, I like the look of the silverstone ML03B but I think I cannot fit a grapchic card in it. I'm, trying to make this very similar to a steam machine.
The Silverstone ML05 can take a low profile GPU and it looks like a DVD player/receiver. It's the case I chose for my recent HTPC build. Very happy with it.
The CM 130 and Air240 are both on the large/chunky side for mITX cases - meant more for gaming rigs where you need to fit a full sized GPU and it will be sitting on your desk etc.
IMO, an HTPC should be much smaller and thinner. Unless you're playing demanding games directly on the HTPC, you shouldn't need anything crazy on the GPU side - APUs with decent iGPU is more than enough for media center duties and in-home game streaming through steam.
Well, I went with the Athlon 5350 quad core APU that has a TDP of 25 watts and the motherboard I chose - the ASRock AM1H-ITX, has a 19V DC power in for using a laptop power brick. So I'm using a Cooler Master NA90 90watt 19V universal external laptop PSU/charger.
Since you're running a 7850k, you'll need a beefier PSU. Any SFX PSU from 300-450 watts from seasonic or silverstone will do just fine.