The audio signal coming out of a keyboard has all the same characteristics as the signal coming out of a CD player's line-out socket. For home use you just need the same kind of speakers/amplifier as you would use for a CD player.
A hi-fi system, or a pair of powered PC speakers will do the job nicely.
The "keyboard equivalent" of a guitar amp -- something the same size and shape as a guitar amp, but suitable for a keyboard -- is often called a "keyboard amp". The difference between a keyboard amp and a guitar amp is:
- The guitar amp is designed to add colour and sometimes distortion to the sound. The keyboard amp is designed to accurately reproduce the output of the keyboard
- The guitar amp is designed for the low-level output of a guitar pickup. The keyboard amp is designed for the line-level output of a keyboard.
- The guitar amp -- both its amplifier and its speaker - are designed for the relatively narrow range of frequencies that a guitar produces. The keyboard amp is designed for the full range of frequencies a synth might produce (more or less the whole of the human hearing range)
As it happens, the design goals of the keyboard amp match the goals of a hi-fi amp and speakers, or anything designed for playing back music.
Clearly, a hi-fi with a subwoofer does a better job with the bass in recorded music, than a hi-fi with only small speakers. The same applies when amplifying music from a keyboard.
For combining two inputs into one amplifier, the very simplest option is a splitter (used as a combiner) like this:
There are theoretical reasons why this might not give the best quality -- but it has always worked OK for me.
A more sophisticated option is to use a mixer; this will let you adjust levels in one place, may give a cleaner sound, and depending on how much you spend, may give you extra features like compression, stereo balance, an effects loop and so on.