Since your friends have not been to Bangkok I think I would spend time there seeing the main sights at least. It would be a shame to go through BKK and not see the Grand Palace and the other biggies. (as long as the situation isn't out of control) But I am an admitted Bangkok lover.

I thought Vietnam was OK and certainly enjoyed the time around Hanoi. 3 (really 2.5 at most) days is not much time. You'd need to arrange a visa as well.

If I were you I think I would just split the time between Cambodia and Thailand. You say that you are young, so I would say expect to go back to the region at some point. Vietnam could easily take up 2 weeks on it own.

My first trip to SE Asia I spent 3 weeks in Thailand. Period. The next year I went back and added in Siem Reap and Phnom Penh. The next year I added southern Cambodia and Laos along with more time in Thailand. Etc.