I heard that Bitfinex and Bittrex will give you BCC if you don't move your Bitcoins from these exchanges on 1 August, but I am seriously considering to move them to a new generated paper wallet. What would you recommend, because I also saw video about price drops that could occur after hard fork. Please let me know your thoughts and what can happen after the USHF.
You will not face any issue if you will keep your Bitcoins on Bittrex or Bitfinex as they both have decided to support BCC. It is completely fine. Your Bitcoins will remain safe and you will get BCC as well, after 1st August. In general (keeping all the fork thing aside) it is not advisable to keep your Bitcoin on exchange unless you want to do trading. Hardware or software wallets are always better in terms of security and thus preferred if you only want to hold your Bitcoins.