Hardware wallets
So if you want to store Bitcoin in a wallet there are 2 main ways of doing so. You can either have a hardware wallet meaning it is a physical electronic device. This is the safest way to store Bitcoin or any other coin since the only way to withdraw/spend the currency is by connecting it to a device such as a laptop or phone.
The most commonly used hardware wallets are;
• Ledger Nano S
• Trezor
• Keepkey
I personally like the Ledger Nano Z the best and I believe the overall community agrees on this. The Ledger Nano S is the most affordable hardware wallet that comes with a screen and it is very easy to set up on any desktop computer. If you are to lose the hardware wallet you can recover your coins using a 24 word passphrase you receive when setting it up (would recommend noting down this phrase on paper).
Ps. if you are buying a hardware wallet make sure to get one that is bough directly from the company and now from ebay or such since there are hacked devices out there that scam buyers and steal their coins.
The advantage pros of hardware wallets is that they are probably the easiest way to secure your crypto currencies and there is less margin for error. However a disadvantage is that they cost.
I would recommend hardware wallets to anyone who is serious about security and convenience.
Hot wallets
The second type of wallet is hot wallets which are wallets that run on devices that are connected to the internet like phones or computers. They are the easiest way to store your currencies and sending/receiving coins is fast and convenient. Only issue with hot wallets is that it could be argued they are not as safe when handling larger quantities since the private keys are online generated and not offline like the hardware wallets.
For the iPhone I recommend breadwallet.
Very easy to use and gives users full control over their private keys.
As for the computer I recommend Exodus and Electrum. I personally use Exodus as it can hold a large variety of coins and is very easy to use. Both offer their service for both mac and PC.