First, welcome to the Forum!
A receiver and a good pair of speakers for $100-200? That’s unrealistically optimistic, even talking used equipment.
I’d suggest ditching the receiver. It’s not needed for a computer system and has all kinds of things that you don’t have a use for that are just money wasted, such as an AM/FM tuner, pre-amplifier, capability for multiple inputs, and if it’s an AVR, then video and Dolby Digital processing, etc. If you're broke then you sure don't want to be wasting money on stuff you don't need anyway. All you really need from it is the amplifier to power the speakers.
Since all you really need is an amplifier and speakers, here’s a thought: Yust get a pair of active (powered) speakers. You can get decent active speakers under $200, such as the Audioengine A2, especially if you look for used, Others will probably chime in with recommendations.
As far as a sub, I’d suggest Craigslisting a something at least 10” from a name brand like Paradigm or Velodyne. It should be no problem finding something under $200.
If you’re worried how to connect both a sub and active speakers to the computer, all you need to do is split the audio output.
Hope this helps.
Regards,
Wayne A. Pflughaupt