I don't work for Vietnam Airlines, but I live in Ho Chi Minh City, and can answer your question about taxis.
Yes, almost all expats take taxis, and they are the safest form of transport available, as most people are on scooters. Taxis are cheap. From the airport to downtown will cost about 120000 dong, less than $6 USD
You can also take xe om, a scooter taxi. These can be fun, but I recommend getting to know the guy first, pick an older gentleman as they ride slower and more carefully, and not to use any xe om by the airport as they are overpriced.
You should also look into VietJet. It's a private company and I hear the pay is much better. They are also growing at a faster rate than Vietnam Airlines, fly A320s and employ lots of E. European pilots.