Yes, you will need a compatible wallet to store your cryptocurrency. Most exchanges offer all users a non-custodial wallet free of charge, and if the exchange is regulated, these are reasonably safe. However, if you are planning to purchase a lot of cryptocurrencies, or hold them over a long period of time, we would recommend you have your own private wallet. There are many to choose from, but a hardware option that stores your investment offline is by far the safest option.