With Coinbase am I ok? Or should i use another kind of wallet?
CoinBase is online wallet - can you get the private key to it? If so, than CoinBase is quite OK, but better use the desktop wallet if you want to have the coins in both blockchains in the case of split.
From the other hand Coinbase will surely stay with the winner, so you will likely keep the value of your holdings.
Is it safe to convert BTC balance in Bittrex into USD Tether until the situation clears up?
If you don't need marginal splitcoin and sure about the BTC rate - than you could keep BTC without any conversion.
PS
by the way, Tether USD uses BTC blockchain, so better not to use it during the possible split turmoil
