I have my bitcoin both on bittrex and blockchain.info, will they support the upcoming forks and give me the free coins? If they would not, where would you suggest I move my coins to? Thanks as you respond.
Blockchain.info will inderectly give you an option to have "free coins" from any future fork. Blockchain.info give you the option to export your private keys (this is done by giving you some random words - mnemonic seed). With this seed you can generate your private keys afterwoeds with private keys you can claim any future split/fork if it occurs. But please read first about private keys and understand the risk when you play with them, try to do it on an offline enviroment - if you ask me I'd chose some live CD OS in an offline mode for security.
Honestly I don't know about bittrex but it is not ADVISED TO KEEP YOUR COINS ON EXCHANGES - keep in mind this. Why you ask? Simply because you don't have the right to your private keys which means coins are not yours.
Also depends if any wallet provider will add support to forks. I know about coinomi that they supported all hard forks till now (can read even their posts on medium about claiming them if you used coinomi
https://medium.com/@coinomi) although they are only available for android.
Another widley used wallet - exodus for instace don't support bitcoin gold now, although since you have your private keys with exodus you can extract them and import to one wallet that supports bitcoin gold same applies to another popular multi coin wallet jaxx...
So yeah just use an wallet that provides you with private keys, I personally love electrum for bitcoin as it provides many features and gives me the ability to see my private keys so I can in future, if needed, to "claim free coins from hard forks" if they ever happen.