If you really want to have a secure wallet, I recommend downloading a wallet onto an external drive; hard-drive, solid-state, USB stick, whatever you think would work, then make multiple copies of it and have them all stored securely and in different locations you're aware of, so you can always make sure you have a backup in case something happens to one of the drives. If you want you can go a set further and get something like Electrum for your wallet and use the various passwords and security features on top of having a bunch of drives.

Alternatively, use an online service like blockchain.info, which has a lot of security features. But be aware that you are leaving your Bitcoin in someone else's hands and you have to hope it all goes well, they only have a guarantee of making your Bitcoin safe so their own business can grow.