The closest you'll get in terms of price & size will be Steam Machine under base configurations. While most Steam Machines will be released in November, there's 2 that are on the market right now.
The Alienware Alpha / Steam Machine i3 ( http://www.dell.com/us/p/alienware-alpha/pd ) & the Syber Steam Machine I ( http://www.sybergaming.com/products/steam-machine.aspx ). Each system, under base configurations, run around $500 (although you may find them for less). While the Alienware Alphas runs on Windows 8.1 (upgradable to Windows 10), The Alienware Steam Machines & Syber Steam Machines will be running on Steam OS.
The Alienware Alpha, which I own the i7 configuration (highest available option), is a little larger than the original Wii (so it's definitively smaller than a PS4) & includes the following:
* 2 GB custom Nvidia graphics card (sorry, can't remember the exact model number)
* 5 USB ports, 2 USB 2.0 ports on front, 2 USB 3.0 ports on the back, 1 USB 2.0 port underneath (hidden under an access panel).
* Internal BlueTooth card
* Internal WiFi (802.11.ac) card
* Ethernet port (for wired connections)
* HDMI out & PASSTHROUGH ports
* Wireless XBox 360 controller
* USB XBox 360 wireless controller receiver
The main differences between the configurations are HDD space, processor & RAM... but the Alpha does allow you to modify your Alpha & upgrade these components as you desire.
The Alpha is designed to work with just 360 controller & has custom software (formerly AlienwareUI, NOW HiveMindUI) to accommodate it, but I recommend investing $30 in a Logitech K400r wireless keyboard + trackpad combo so you can use it like a regular computer when you want... OR when a game controller isn't the best option. I will mention that the Alienware Steam Machine is just a rebranded Alpha that's running Steam OS & has the Steam Controller (instead of the XBox 360 controller).
While performance will vary based on your hardware configurations, it'll run PC games at 720 or 1080p at acceptable speeds (30 fps or higher) under default settings for most games. HOWEVER, more graphically intensive games (like GTA V) may need some additional work for optimal performance.
Hope this helps!