What's my best option here regarding the current fees ?
What's your wallet? If you have Electrum or Bitcoin Core, use the wallet's estimate. If not, go to bitcoinfees.earn.com and select the fee you wish to include. You have to manually adjust it according to your wallet (ie. satoshi/byte or BTC/byte or BTC/KB)
Should I first send BTC to Electrum Segwit wallet and then to GDAX or should send it directly ?
Directly. If you were to send the BTC to a Segwit address first, you will pay the fees for the transfer and then again when you send it to GDAX.
Is GDAX compatible with Segwit wallets ?
Thanks in advance.
Yes. Segwit transactions are backwards compatible. You shouldn't have any problems.