Thank you for your answer. I will head down to the local sports store and see if I can find a good pair of beginner basketball shoes.Just get some Chuck Taylor's, Converse. If you're starting out, you might as well get something you can also wear day to day.
Alternatively, hit up a local sports store and find whatever is on sale and offers a good level of protection for your ankle, while also feeling mobile. Nike, Adidas, And1, Air Jordan and even the likes of Under Armour and Reebok have a few decent offerings.