1. Build a very small system using one of those Intel Atom motherboards like this, which come with the Atom processors attached. Get the smallest CPU casing for it. Or get someone to custom build one.
2. Get one of those micro USB card readers with a micro SD card, or get a small USB drive.
3. Install a very light Linux distro on the microSD card or the USB drive, and customize the distro to load only Dosbox with it's core required dependencies.
If required, install a Dosbox frontend and make the Linux boot directly into the frontend (for Linux - DBGL).
Set the BIOS to boot into USB first.
4. If a frontend is installed, then install Joy2Key for Linux - you can assign keyboard commands to the gamepad/joystick.
5. Once this is done, you can select the games which will be displayed in the frontend via the gamepad or joystick directly, without the need to use a keyboard.
Advantages :
Using the motherboard enables the user to add USB peripherals whenever required. Also enables easy USB joystick/gamepad installation. It has on board video, so no need to install additional graphics card, which may take up the smallest space as desired for a 'Dos console'.
Linux and Dosbox for Linux takes care of all the hassles of sound card 'installation' and speed control.
As such, a Dosbox frontend is highly recommended, especially if a console-like experience is desired to use the gamepad as the main controller.
This enables to the user to use the gamepad in conjunction with the Joy2Key mapper utility. If extra buttons are present on the gamepad, it may be possible to assign Ctrl-F9 to quit the running game back to the frontend to choose another game to load.
Also you can emulate mouse buttons with the joy2key.
Disadvantages :
A streamlined Linux package just for running Dosbox with it's core dependencies is required. Requires knowledge to make that distro to boot directly into Dosbox, or a frontend. I think this can be done easily by those who know how. Preferably a new distro built for this purpose will be wonderful.
A streamlined Linux will be a lot easier on system resources than Windows.
I haven't used Joy2Key for sometime now, and that too I've only used the Windows version. I hope you can assign the key-press combinations with ease.
'Dos Console' will be limited to the Arcade and Action games for Dos. Other games are best played with the keyboard + mouse, which shouldn't be a problem if using the motherboards as mentioned above - which come with free USB slots.
Of course, the games have to be installed first on another system after installing the Linux Distro with Dosbox and the frontends.
Alternately, you can install a 2.5" hard drive, but may require proper HDD holder within the small casing.
Preferably a double-decker like CPU case will be helpful to install the Power Supply at the bottom and the motherboard on the top decker, or vice versa, so as not to elongate or enlarge the cpu case too much.