IMO, $200 is probably a tough price point to achieve if you want a new bike in most parts of the World ... heck, you could easily spend $200 on just a set of "Track" hubs.
However, if you can DIY, you can certainly buy a used, vintage bike & convert it for use as a Fixie-or-SS for under $200.
Others have suggested otherwise, but I will tell you that CHAINLINE matters ...
- in addition to resistance, or lack of
- you need to be concerned with the chain staying engaged or crawling off the teeth
and, a good chainline ensures a minimum amount of resistance and that the chain will stay engaged.
If the vintage bike has a Freewheel which you replace with either a BMX Freewheel or a Track Cog, you will want to
redish the rear wheel ...
If the bike has a Freehub & uses a cassette, then you can simply use spacers to line up the cog.
- you can cut "spacers" from appropriately sized PVC tubing
BTW. I've seen Fixies for just over $200
[COLOR= #ff0000]+ shipping[/COLOR] on eBay. They are certainly good-enough for most riders for most situations ... the hub quality & BB quality are unknown, however ...
et cetera.