Is mining hardware particular to specific mining algorithm(s)? In particular, I was pool-mining with scrypt algorithm, using my GPU (was not bitcoin, but another coin named gamecredits, at gmc.acidpool.com).

I would like to purchase cheap mining hawdware (which would be useless with bitcoin but perhaps good with relatively "new" coins). Should I care whether a hardware supports "scrypt" in this case? Or does hardware care about a more "primitive" level without caring about the algorithm?
Different currencies have different mining algorithms. What you should do is to use coinwarz.com to calculate the most profitable one, by filling in the details of the mining hardware's specs of the miners you're thinking about buying.

Be sure to put cryptocurrencies' future values (predict them!) and when the next miner may be released (predict!) into account (which coinwarz can't)