A wallet, like the name implies, is the digital version of the real life item. To be able to send and receive CryptoCurrency you need a wallet. It is used to store your a digital keys and hence your CryptoCurrency coins.
A wallet address is used by the sender as a place to send your crypto, think of it as being similar to an email address which where someone can send your electronic mail to. To receive your crypto in your “wallet” you would give the person sending you money a wallet address `that you control.
As a general rule of thumb each coin has its own wallet software, however there are also wallets that can house various CryptoCurrencies. Decide on which CryptoCurrency you wish to purchase and then proceed to download the required wallet to store your purchase. Should you wish to send your CryptoCurrency to someone else then get them to also download their own wallet and then send you their address. Do not exchange your wallet private keys with each other.