I earn bitcoin from faucets. I'm using blockchain wallet. And I have 0.0008+ btc on my blockchain wallet. When I try to sent my bitcoin to other address it only allow me to sent nearly 0.00026 btc. It means I have to pay 0.00054+ btc for this transaction fee.

My question is which wallet I should use?
I earn bitcoin from faucets. Not so much btc I can earn from faucet. To keep my btc safe and avoid the high transaction fee which wallet I should use?
Which wallet is best in all means?