Normal fees means default fees right. That would set as by default and nowadays default fees has been increased to 0.0007 to 0.00092 btc for a transaction in blockchain.info and coinbase. If you wish to have a low fees for a transaction. you can use the the multibit or bitcoincore to have a fees as 0.0001 or little. Confirmation time would little longer than the above mentioned one.
We can set our desired fee when using blockchain wallet too but frankly if we used low fees, below 100 sat/B, there's a chance for our transaction to get confirmed after several days. It's better to use medium or higher fee if we are in a hurry.