Here is what I have learned in the last day...
Visa Options for US Citizens
1. One month, one entry
2. One month, multiple entries
3. Three months, one entry
4. Three months, multiple entries
5. One year, multiple entries
Everyone needs an e-visa approval before boarding if they will enter the country. (e.g. clear customs). Connecting flights - even on separate tickets - do not require a visa IF IF IF the connecting airline has a counter in the transit area. (The airline may have their own rules.) Going back to the same country is not allowed without clearing customs first.
Expect the visa check at your point of departure. (Computer will flag your ticket.) The actual stamp is received on arrival (in most cases). (There is also the possibility of a visa insert with no need to go to 'visa on arrival'.)
Official Site:
Embassy of the Socialist Republic of Vietnam in the United States
For me, they have been very quick in their responses. (We have multiple tickets throughout the year so opted for the 1-year multiple entry visa.) After submitting your application you will get an email confirmation. You are asked to send them a text message. A few hours later we got a text back with the cost; $400 for two annual visas including all costs. The last email says 3-day service including FedEx overnight delivery. So we are expecting our visas next week.