Luke's comment is a good place to start. I might add: there are lots of kinds of synthesizers. Many don't have keyboards. You really need to start out by figuring out what it is you want to do. Do you want to play tonal music (e.g. classical instruments or a digital keyboard) or just create wild sounds with a theremin or jazzed-up drum machine, for examples. It's trivial to run the output of a digital piano through an "effects processor" kit to get all sorts of interesting sounds (on-pitch), if that's what you're thinking of. Just keep in mind that Rick Wakeman was an accomplished pianist before he laid out his 12 synth keyboards around him.