Options for replacing a 7 speed Shimano cassette / chain
You don't need to buy NOS. 7 speed cassettes are still manufactured, we stock them and they start at $20 all the way up to $36 for a Shimano HG50 which comes in 12-28. Go with a matching Shimano HG50 chain.

Unless you buy a new rear wheel, you cannot go above 7 speed. 7 speed freehub bodies are shorter than 8+ speed freehub bodies. An 8+ speed cassette is too wide to fit your freehub.