I think you have the list above.

Flying within Vietnam (domestic flights) ypu will likely be flying either Vietnam or Vietjet (there can be other options depending on the route but those are the usual options). If you just want to get on the plane - doesn't matter where you sit etc then it will all be fine. If you care where you sit or want to sit with friends - you may want to address that with the agent when you check in and check your bags. The gate agents often do not appear until shortly before departure and by then the options may be very limited.

There are also differences between Vietnam and Vietjet. If you just want the cheapest flight available that it easy but if other things matter to you then you should read up on the differences.