Do not ever keep your bit coins on any bit coin exchange services or hosted bitcoin wallets. These service keep your private keys. One should look for following things while selecting reliable bitcoin wallets--
 1.choose your wallet where you control your private keys.
 2.Wallet having seed backup keys and pin codes.
        Based on what medium user wants to use bit coins wallets can be classified as
        Mobile wallets
        Desktop wallets
        Hardware wallets
        Web wallets
        Paper wallets
 The wallet one should use is depend on level of one's activity and level of security with which one want to handle their bitcoin. Also depend on how much you want to store and how frequently want to use your funds.
  To store significant amount of bitcoin I prefer hardware wallets like Ledger Nano X, Trezor
  Use desktop wallets if not doing daily transactions like exodus, electrum, bitcoin core
  Use mobile wallets to store small amount of coin and for daily transactions like edge, trust wallet, blockchain
   You can use web wallets like coin base , finance for small transactions.