Since you currently have a working 8-speed, then you are virtually certain to have 130 rear spacing. You can measure with a good metal ruler easily, or get some digital calipers, but your wheels and your current gearing indicate you don't need to be concerned about the rear dropout spacing.

As for your original question, I can't imagine for $50 you can get anything functional as a group set. What's your absolute top budget for this project? Maybe post a photo of your current bike, along with a description of the current components, and give a price range you're looking to hit. The board might be able to help you find exactly what you need at a great price.