You mentioned that blockchain.info is good for small amounts. How small would these amounts be?
That depends on the individual. Consider the amount that you need to have immediate access to while you are out, or the amount that wouldn't devastate you if you lost it to a hacker.
Essentially, think about an actual wallet in your pocket. How much cash would you feel comfortable carrying around in that wallet while in a large crowd full of pick-pockets?
What if a person wanted to store larger amounts than the small amounts you refer to? What would they do?
What do you do with your cash when you go out somewhere and you aren't comfortable carrying large amounts of cash with you? You typically leave the excess cash at home? Perhaps in a safe?
Consider learning about paper wallets, or at least installing a wallet on your home computer such as Armory, Bitcoin-Qt, or MultiBit.