If you want to assure that you will receive the Bitcoin Gold coins after the fork, you will need to withdraw your coins from Bittrex and store them in a wallet which you may have full control over the private keys.
Do this before October 25 (the day the fork is happening):
1. Download Electrum[1] (recommended)
2. Create a new wallet and send every Bitcoin you have at any exchange to this new wallet.
3. Wait until the fork happens.
4. Now this wallet has x BTC and the same amount in BTG.5. When it's safe to spend your coins, send your Bitcoins to any place you want (including an exchange);
6. Now this wallet only has x BTG and no BTC.7. Download a valid Bitcoin Gold wallet and import the private key that still contains the BTG coins.
8. Send them to an exchange if you want to sell those coins.
[1]
https://electrum.org/