I would get a Raspberry Pi 3, either standalone or as a kit. You'll pretty much need the little necessities if you don't go with a kit; like SD card, HDMi cable, case, a USB gamepad and at least a 2.5 Amp mini USB power adapter. The majority of the things can be sourced for cheap if you look. Presumably you'll already have a monitor/tv and usb keyboard needed for configuration. Check this
recent thread over at Redflagdeals concerning the RPi3.
Once acquired, I'd suggested going to the
RetroPie site. Download the current RetroPie image, write it to the SD card. Plug it in, along with the USB gamepad, configured the controller on boot and put roms (games) in the appropriate folder. If you have the RPi on your network, you'll be able to browse and drop roms in the specific folder. There's gonna be a folder for each type of emulator, NES, SNES, Genesis, etc.. If you have problems, Google is your friend and be sure to check the RetroPie help forum.
I did not intend to make it sound like it's easy and most certainly you'll need to put some of effort, depending on your ease with this sort of thing. Of course it's a personally choice if it's all worth your time or not. Let me know if you have any specific questions.
The RPi is a seriously versatile little computer. If Kodi is not your thing and you'll a little savvy (or willing to learn) you can do just about anything with a RPi; tons of projects out there and a great community to boot. I built a
home monitoring system with an old Pi I had laying around. There's a plethora of sensors that can be connected to it and programmable libraries (in Python) that can be used to communicate with them. In short the Pi is a great educational device for everyone, children especially, used as a great introduction to the world of computers and programming.
