You need at least two weeks to visit these two countries; if you have more time you can include Laos and Thailand as well (Indochina is a big area indeed including Myanmar, Thailand, the Malaysian peninsula, Laos, Vietnam and Cambodia).
Your first stop in Vietnam will be either Saigon or Hanoi. You may find Hanoi historically more charming and Saigon a little tiring and humid. The ancient city of Hue and the little picturesque town of Hoi An will appeal more to your tastes if you are looking something calm and authentic. The famous Halong Bay will definitely be the highlight of your travel and considering the 4 hour drive form Hanoi spending a night in the boat is highly recommended- it is also the perfect way to enjoy every hour of the sun shine, you will admire the shades during the sun rise. If you are planning to do trekking the best place would be Sapa in the north so be prepared for a colder climate.
You can book direct flights with budget fares from Ho Chi Minh City (Saigon) to Hue, to Hoi An, to Hanoi, from Hanoi to Siem Reap in Cambodia and from Siem Reap to Bangkok; this will save you a lot of time. Your daily costs such as food, taxi, etc. will be quite economic; bargains are recommended when you take a taxi or a tuktuk.
As for Cambodia’s famous Angkor Wat, you will need to fly to siem Reap (either from Hanoi or Bangkok). It is actually not just one temple. You will be surprised to see hundreds of them, you will need at least three days to visit the most important ones. The entrance tickets are sold as one day or four day tickets; you can rent a bike from your hotel and enjoy the scenery more while pedalling from one temple to another. For some temples such as Banteay Srei you will need a car as it is far from the other ones and reaching there by bike will be quite difficult. Most of the temples are worth a visit but you will probably visit Angkor Wat more than once to watch the sunrise and will be shocked to witness hundreds of tourists’ with their tripods to take the best shot.
Some books to read before you go: Denise Chong’s ‘The Girl in the Picture’ tells the story of the most iconic picture of the Vietnam war. French writer André Mauraux’s ‘The way of the Kings’ is an adventure novel, he himself was taken into custody during his years in Cambodia because of smuggling a historical artifact.
Lastly, do not forget to spend sometime in Bangkok if you have a stopover there. See our detailed collection.