There are several types of wallets available for you to download to hold your Zcash.
Internet Wallets – Are the fastest way to start accepting Zcash. Many of the websites below also have an App you can download for your phone to manage your Zcash. Be sure to use strong passwords and enable 2-factor authentication when it is available. CryptoCompare has a nice guide to help you research before choosing.
Hardware Wallets – Hardware wallets are the safest way to store your Zcash and other cryptocurrencies. The main drawback (for now) is that they only support Zcash Transparent Addresses and they cost between $79-$139. You purchase a physical device which has a number of safeguards to prevent theft and have emergency steps you can take to recover your Zcash if your device is lost:
Local Wallets – These Wallets run the Zcash client and a full network node on your Computer. These are a little more technical to set-up and use. To use Zcashs Private Addresses you will need to download one of these:
Note: The first link above is for the Official Zcash Client, the Windows release is from David Mercier and Kozyilmaz has the most up-to date Mac version. There is a good Tutorial for the Windows wallet on Coinwallet Guide.com. Be sure to perform regular Backups of your wallet. You can find a list of the API commands to use with these Zcash wallets Here
If you like to dig into code there are some very cool Zcash wallet projects that you can use:
Exchange Wallets – Exchange wallets are one of the easiest to set up because all you have to do is create an account with one of the many Exchanges that support Zcash. After you create an account it is very simple to generate an address to receive/spend or trade Zcash. At the moment only one exchange Shapeshift.io supports payment to Private Addresses
IMPORTANT: The most important thing you need to keep in mind about wallets is that by using a wallet (whether on your own computer, on an app, or on an exchange) YOU are acting as your own Bank. If you lose, misplace, forget your password, or are somehow hacked then your Zcash will be lost forever. Be very careful when dealing with wallets be sure to perform regular Backups and always use strong passwords to help protect yourself.
Here are a few videos explaining how to create and use the different types of wallets: