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.