As different Crypto-Currencies have different underlying Algorithms (e.g. SHA256, Scrypt, CryptoNight, etc : Source). Does this mean that if I am looking to buy cryptocurrency mining hardware, I need to decide the hardware after I decide which currency I am looking to mine? For example, a GPU setup may be good for Ethereum but for LiteCoin, I need some ASIC hardware?
Yes, it is true that different coins can require entirely different mining hardware. Some coins use sha, scrypt or some other algorithm; others use a different protocol altogether; and some are privately mined and can only be purchased.
If you want to participate in mining, you need to settle on a coin first. One consideration is whether the hardware for that coin can easily be turned toward a different coin. A lot of coins use sha or scrypt, so you'll have a lot of choices if you choose one of those.
After that comes the difficult and highly speculative part: the profit analysis. Good luck and happy mining.