Pick the following:

Case: Tower(PC) or any other console( PS4, Xbox, Wii U, Gamecube, Atari, etc) Looks always matter

Design: Colour? Special designs? Badass features such as glowing in the dark?

OS: Windows, Mac OS, 3ds OS, Playstation OS, Wii U OS...you get the point

Controller: Keyboard, Xbox controller, Pro controller(Wii U), Duelshock, etc

Exclusives: From any game company, which would you pick to make exclusive games for your device? Examples are Nintendo, Sony, Microsoft, Sega, Telltale, Square Enix, etc.

Specs: Would you go all out and get god-like performance? Or are you fine with more modest results?

Special feature: You obviously need something to go along with your dandy machine. Motion control, VR, duel screens, 3D, AR, etc.

Name: You obviously need a name. Can't just call it a gaming machine all the time.

Example:

Case: PS4

Design: Shiny Aegislash themed- mixture of black and red, with the shield showing on the top. 

OS: Mac OS/Wii U OS

Controller: Pro controller(Keyboard for 5% of the time)

Exclusives: Nintendo

Specs: Modest, capable of reaching 720p @ 60 fps for the majority of games(even demanding ones)

Special feature: Pricing of digital games changes with retail version as well. For example, if the average price for a new mario game went from 40 to 25, the digital game's price will decrease as well. Also, digital games are 5-10% cheaper due to the fact that they have huge noticeable cons that retail games don't have.

Name:  Revolution

Pricing: 300

case: PS4 (or slightly bigger if needed for cooling)
design: Black/White/Red, maybe so top-down it looked like their Square enix's Logo.
OS: Linux base (vulkan based games)
Controller: Dual Shock 4
Exclusive: Square Enix
Specs: ~5.5 Teraflop gpu perf ( x86 cpu, Zen part from amd, so it has a strong cpu).
Special feature: Has a PS-plus like subcription that gives you access to all their MMOs & Online games.
Name: the "SE" box. / SE-box.
Price: 399$

I made my own blueprints since 2004 to make my own gaming machine for id software games exclusively(and so modded games or powered by id tech games).

I'm still looking for better components because the modders would make bigger custom maps or other stuff for Doom & Quake, i'm not kidding.

EDIT: This is something i want make.

Case: Black PC mini itx case

Design: Red "Q" logo on top like this: https://upload.wikimedia.org/wikipedia/commons/e/e6/Quake_Q_logo.png

OS: Windows 7

Controller: Steam controller & keyboard/mouse

Exclusive: id Software

Spec: AMD APU 2.5Ghz, 4GB DDR3 RAM

Special feature: download free custom maps, free/buy modded games & free multiplayer online

Name: Cyberdemon(i dunno xD)

Pricing: $200

I already made one though, it sits on my desk at home
No but in all honesty I used to love designing handhelds when I was younger.

Case: PS4
Design: custom KITT design that has the red light just like the car, with different movements for different things. Also, it makes KITT sounds.
OS: modded PS4 OS with additional features such as folders!
Controller: DS4 elite controller
Exclusives: Sony, Nintendo, Sega, PG, From and Capcom
Specs: upgraded Cell with 12GB DDR5X
Special feature: ability to use any decent mobile phone as a screen.
Name: PS KITT
Pricing: 350

+

Deliver 100 million units back in time to June 1996, plz. 

To Hiroshi Yamauchi. 

Care of: Your fanbase from the future. 

whoa there buddy, only one company :P

That's should have been, but describing, i made my own custom PS1 with Intel Nuc kit + linux OS + DS4 20th anniversary and my PS1 games collection are ripped from discs to sd cards.

Too much info to put in but I'll summarize. Or at least cover a few points.

I don't believe in having a gaming PC, I think it's too inefficient. Too much fat.

So I'll go for a console form factor more like the PS4/XB1s.

It's all in the board tho, Have an 8 core 2Ghz-2.5Ghz CPU with 2 cores reserved for the OS and 6 cores for apps and a 5TF GPU couple with 10GB or 250GB/s+ RAM with 2 GB reserved for the OS.

now the most important bit is I'll build 1TB of nand flash storage directly onto the board connected to system ram with a 16x PCiE ver 3 bus which would allow for 20GB/s+ bandwidth between internal storage and system ram.

There will be a 2.5 sata 3 slot but the console will not come wit a HDD, that will be up to the user and only serve as a storage/backup drive.

I'll go with a PS4 controller complete with track pad.

I'll require all games to be built natively at 1080p at a locked 60fps and have a dedicated upscaled chip for 4k support. But above all else, it will be a super snappy console with absolutely zero load times for anything.