Bitcoin wallets is where you store your bitcoins. Without them, you cannot use bitcoins. But, selecting a secure wallet is important. In fact, most important.. Because, losing bitcoins means burning cash.
Now, according to my usage and researches and what I have found. These are the wallets which i found trusted and useful.
(1) Coinbase- they provide more privacy as they have their own privacy team separately. Best thing is that transactions are completely tax free.
(2) Blockchain- It has got the most number of usets. So no doubt on security. It's trusted most by miners too.
(3) Mycelium wallet- It's git very low transaction fees and provides the best backup system for private keys. You can use multiple wallets at once.
1) Coinbase pays the transaction fees for the customers but their Terms of Service restrict some kind of transactions and your account will be suspended if the coins are linked with it.
2) Nothing indicates that Blockchain.info is trusted by miners. In fact, many users have gone against it.
3) Any desktop/phone wallet should allow the users to use their address repeatedly and can use another one simultaneously.