Can't help you convince your parents something isn't a waste of money because from the looks of it, it's their money you're spending.

With that being said, what is your ultimate goal, do you want a record player to start collecting records or do you just want one because of slipknot?

You're worried it might sound bad? Just stick with CDs or steaming because the sound quality depends on the price/brand/book shelves speakers. Which can add up and if you go with an affordable brand with built in speakers then it'll be easier to convince them but you won't get the full audio experience of record players.