Somebody told me its safe to safe my bitcoin to local bitcoin wallet. is it true?
you talking about the site localbitcoins.com its not true that safe to store your Bitcoin on their wallet.
and i currently known blockchain its the high security level bitcoin wallet but the transaction fees make me want to cry.
If you like a Bitcoin wallet that you have a control of the transaction fees just use electrum( desktop wallet ) or mycelium wallet for mobile they have features that you can choose how much fees you want to include in your transactions.
But is better to include a higher fee than a smaller fee to avoid problems like stuck transaction.