The advent of powered speakers has all but killing the low end audio amp, but if you hunt ebay and places like that you can get DIY stereo amps for under 20 bucks, but I seriously doubt that is a good option, and from 50-200 there is a small number of nice little stereo amps, but none of them will give you a sub-output, that needs to be done by the pre-amp, and it sounds like your TV does not have an output for it.
In most cases it has turned out better and cheaper for folks to just get a set of powered speakers, they are very cheap these days. Also a low end reciever or boom-box is also an option that tends to give you more bang fir the buck and in the case if a 100 buck receiver you'll get your sub-out as well.
However if you are stuck omn a sereo amp, that link to ebay above will get you in the right neighborhood.
Also note that you can pick up a used receiver with all the bells and whistles again for under 100 bucks.