Even if the wallet is considered 'ready' and 'safe', you should still store it in a local wallet to ensure 100% safety, and I recommend you to do it before it comes. I've also made the switch from an online exchange wallet to a desktop wallet (Electrum), and I suggest you do the same.
No matter who you support (BTC or BTU) you should make sure your coins are on a self hosted wallet (one that you control the private keys to). Examples of such wallets are Electrum and Exodus.
If you have a substantial amount of Bitcoins use TREZOR or Ledger for maximum security. This way if a fork does happen you will own both currencies and won’t need to succumb to any exchange or wallet desires.
-99Bitcoins
Good read, I support off chain transactions too, especially for micro-transactions, which a lower fee would be better. CoinBase also supports off chain transactions and there are no fees if transferred in internal accounts, and I hope Bitcoin will move towards this direction too. Scaling of transactions is really going to be an issue, honestly.