There exists several kinds of wallets, found under Recommended Wallets. Roughly speaking, web wallets require the least amount of knowledge and work to set up but are insecure due to phishing, malware, etc.; ordinary wallets for computers and android phones require more knowledge but are more secure and have more options for usage; paper wallets are 100 % secure when generated in a secure manner but the funds are harder to access. For a guide to generate paper wallets, see Creating Paper Wallets.
Ordinary wallets stored on your computer and smart phone are superior in security to that of web wallets, and should always be preferred.
Note that an exchanger SHOULD NOT be used as a wallet.