Question about wallet.

I'm relatively new to bitcoin and the reddit has been super helpful. My question is, I am using a trading software, bitstamp, to buy btc. As far as I can tell, the money is "kept" by the app. I can add money to buy and put money, when I sell, back into my own bank account.

Since I'm new to the game and am working with under 2k...do I need a wallet? Is there a risk of keeping it with the app? What's the benefit od using a wallet and should I?

Thanks!