Now computer-based musicians are mostly using "soft-synths," which are programs/applications that _are_ the synthesizer (your keyboard sounds are in the software). So you only need an inexpensive controller to put your fingers on; the computer/software package does the rest.
IF you want a real synthesizer, it will cost you a lot more than 200 USD if you are buying new (you should be thinking $1,000-$3,000 range). And it depends on whether you want analog or digital synthesis (or some other type or combination thereof). But in that case, the _keyboard itself_ has the sound engine in it, not the computer. I would highly recommend the Roland Juno G (probably available on the used market now), or the newer Roland Juno Gi. These units have great traditional instrument (piano, organ, strings, percussion, horns) as well as synthesizer sounds and effects (bloops, bleeps, lazers, buzzes, robotic voices, house/trance/disco, whatever sounds). They also have on-board four or eight-track audio recording, 16-track MIDI recording, and some nice tweakable analog-type features. But that will cost you a lot more than $200.
GJ