Choosing your wallet
In order to deal with any cryptocurrency you need a digital wallet. You can imagin a wallet as the bank account for fiat currencies. The main and crucial difference is that you are in control of that wallet, not a third party institution.
There are many online sites offering you their services to deal with your digital money but you should only trust those which offer you to generate a private key when you set up the account. In this crypto world, having control of your private key is the only way you can be sure you are the one in contro with your digital money, do not trust any service which does not offer you to create a 12 word password sentence or offers you the private key to your publick key.
I am not intending to endorse any particular service but walleds as Jaxx (offering multi cryptocurrency services), MyEtherWallet for Ether or MyMonero for Monero are good examples of the kind of services you should use.
Finaly, once you start having a considerable amount of money on your porfolio it is very advisable to buy and use a hardware usb wallet like Trezor, LedgerNano or KeePas. Those are problably the most secure wallets you can find right now on the market.
Avoid leaving your money on online exchanges, you have very little control over your money on those sites, just use them whenever you need to exchange or buy a currenty and then transfer your money to your regular wallet.