Most exchanges lack the capability to convert to fiat currencies anything but Bitcoin and Litecoin, some add Primecoin or PPCoin to that list.
But then the Bitcoin mining market is so competitive most miners barely cover their expenses plus there's a very high entry barrier - mining with GPU or CPU is just not worth it anymore.
Litecoin and the other scrypt-based crypto-coins aren't that competitive yet, but those with the biggest market capitalization (like Litecoin and Dogecoin) are approaching that level very quickly, so you'd better have a very energy-efficient cooling system and access to cheap electricity if you want to make money mining them.
Options for you, right now:
Mine for a short time (while difficulty is low) and then hoard a little-known, relatively new coin whom you think has middle-term possibilities. It might be based off something already popular (as Flappycoin) or use a very different algorithm (as megacoin's SHA3 or Vertcoin's scrypt-n). Should this coin become more valuable (as in 5x or 10x or more valuable) you could sell it for BTC, hopefully at a profit.
Join a multipool: you simply provide the hash capabilities of your GPU and the pool's admin gathers all that power to mine the coin deemed the most profitable to mine (taking into account expected block reward and current price in the market). Then pool manager later sells all such acquired coins and pays to you in bitcoins.
Join a merged-mining scrypt pool: You'd be able to mine 42coins, dogecoins, digitalcoin and a few others altogether at the same time so your final hashrate becomes ~25% higher than what you'd get mining just one coin. Of course, you'd need to have multiple wallets and an account at an exchange to sell them afterwards.