Genetic engineering for experimenting at home?
Doing genetic engineering experiments at home is generally referred to as either "biohacking" or "DIY Bio". There's a number of forums out there filled with hobbyists who are doing that sort of work in their homes and garages, and discuss how to do such things in a hobbyist environment. With those terms (and the info in the Wikipedia article), you can probably find those forums on the internet. (Suggestion: look for ones where the regulars emphasize safety and appropriate conduct - not only is it better for you, it's a sign that the regulars know what they're talking about.)

However, 200 USD might be a little small to set up a decent (and safe) "biohacking" space in your own home. Possibly a better bet is to see if you can find a local "makerspace" which has a biology component. Makerspaces are places where, for a small fee, fellow enthusiasts pool together to purchase equipment (and space) to do various projects. Most makerspaces are geared toward the computational/mechanical (e.g. building robots), but there are some out there which have biotech equipment. Your mileage may vary, though, and you're likely to have more success in finding a decent makerspace in a large city than in a small town.

A final caveat is to make sure you research your local laws to figure out what is legal in the jurisdiction you're living. Especially with laws targeting illegal drug production, there are locations where possession of basic scientific equipment by normal homeowners is criminalized. There's also regulations about waste disposal and material storage that you'll need to follow. Also, in most jurisdictions accidents/damage from home labs are penalized much more harshly than, e.g., cooking accidents. Know what's legal/illegal in your jurisdiction (and by your homeowner's insurance) before attempting to set up a home lab.