A good place to start Litecoin is Coinbase. Coinbase is one of the biggest and most respected crypto exchanges out there. They also have some of the lowest fees and you can also use a credit/debit card for purchases if you prefer. Purchases are instantaneous and easy to navigate. It's my preferred place.
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.