First off as far as room. All you need to develop film is a Patterson tank, changing bag, can opener, scizzors, themometer, timer, I use my cellphone, three one liter mixing jugs from the Wal-Mart and chemicals. No darkroom needed. It is so easy you will wonder what stopped you from doing it sooner. As for you budget would that be camera and all ? You can get a developing kit on Ebay fairly cheap.
Chemicals needed. Developer, stop bath, fixer and wash aid. If you are looking for a cheap starter camera maybe an Olympus XA2. They can be had for 30-40 dollars are simple to use and an amazingly fast lens. I would watch YouTube videos on developing. $200.00 would be a tight budget the chemicals will set you back the most.
By the way I would start with just cheap b&w film. Color film or slides are not as easy to work with.