Since you plan to be flying to SE Asia every year now is the time to choose an airline alliance. Star Alliance works well for me. Sign up for the United Explorer card to get the 60000(?) sign-up bonus. Book your flight through united.com with that credit card. Start collecting airline miles.
As an infrequent traveler compared to most people on this site, routing through China is fine, but other routings are preferred. Don't get scared about PEK, although transit for a PEK first timer is no fun.
14 nights, $1000? Your hotel budget is too high. I thought you were looking for a low cost retirement destination? You won't be staying at fancy hotels when you're retired. Might as well start looking at agoda and find a decent place closer to $25 per night. I am not even joking.
Here's a random place that looks fine and is near the tourist area for $28 per night.
https://www.agoda.com/bloom-saigon-h...h-city-vn.html
Keep asking more questions!