I'm looking for an affordable way to avoid perspective distortion when taking selfies. I know the best way to avoid this would be taking a portrait with a DSLR with a 200mm-ish lens from 8 ft away, but this seems too much for me, because of the cost and the setup that requires enough space, a tripod, wifi screen, and remote control. It could be any type of camera, phone, a phone attachment, or whatever. And getting to the subject (myself) as close as I can would be also important since I'll be the one taking a picture of myself.
The most simple answer is a mirror. The distance from the camera to the mirror and back to the subject is optical distance. The additional optical distance will go a long way to reducing most perspective distortion in your selfies or eliminating it altogether.
Perspective distortion is caused by very short (or, in the opposite way, very long) camera to subject distances. When the difference in distance from the camera to the subject's nose and distance to the subjects ears is an appreciable percentage of the first value, the photo looks different than our eyes and brains interpret the same face when viewing it from the same position.
Please note that there is a difference between perspective distortion, caused by the relative positions of the camera and various objects in the field of view and geometric distortion, caused by the way a lens projects a three dimensional world onto a two dimensional sensor or film.
Selfie sticks were designed to solve this specific problem. Most are well within your budget. They require less space than tripods.