What wallet you choose depends on which crypto you want to store, how secure you want to be, and how much you want to spend, among other things.
Not all wallets support all currencies, although for BTC, ETC, LTC, DASH, most do support them. Alt-coins are another story.
For safety, and as the below video and many others suggest, you really need to control your own private keys, otherwise you do not really own the crypto.
Some good, secure wallets are the hardware wallets like the Ledger Nano S, the Trezor, and the KeepKey. But they'll run you somewhere around $100 USD or so. Those wallets are secure even when your computer has been compromised by trojans/viruses,etc.
Then there are always paper wallets: cheap, easy, and secure. Well, at least until you want to spend the crypto on the paper wallet at which point you will have to expose your private key on your mobile phone or your PC.
Keeping your crypto on an online exchange like Coinbase, Kraken, Gemini, etc is not very secure at all. You're at the mercy of those running those exchanges. They could run away with all your crypto if they really wanted to.
And there are many software/mobile wallets like Bread, MyCelium, Exodus, JAXX, and MyEtherWallet. Those are some of the well known and trusted wallets, AKAIK.
This is a rather deep subject, so you'll need to do some homework, but it's well worth it IMHO.
YouTube is your friend in this respect.
Watch this:
@cognoscere Thank you for the detailed reply. I have some bitcoin at coinbase and I need a wallet that I own the private keys , so on Aug 1st when the place @penguinpablo is talking about in this post https://steemit.com/bitcoin/@penguinpablo/bitcoin-cash-is-basically-just-another-altcoin splits the BTC block chain I can get my free BCC , I am pretty sure the wallet I downloaded from Bitcoin.com is a wallet where I own my private keys, but not 100% certain.