I've used Coinbase and Kraken to deposit "real" USD. IMO, Coinbase is easier and if you set up an account at GDAX (uses your Coinbase credentials) you can buy without the high fees. I'm on the fence regarding Kraken as their website and trading platform has been unreliable.

I've only used Bittrex for trading coins. I do not trust Tether since it's not clear to me if it is actually backed by real USD so I avoid trading any pairs matched to USDT and instead tend to use the BTC pairs.