Coinbase is good place to start with buuying Litecoin. Coinbase is one of the biggest and most respected crypto exchanges out there. Plus you can use a credit/debit card if you'd like. Once you've purchased your Litecoins you can send them to GDAX, which is a part of Coinbase and trade them for free.
Here's a link for a $10 bonus to get you started if you want... https://www.coinbase.com/join/5956ef56387e2806cac7ee33?
$10 isn't much, but it's a nice way to get your feet wet and see how the system works.
Good luck and enjoy the profits!