You can travel to Vietnam all year round, there is always nice weather somewhere. :-)
We've been there in late September/early October. The south was hot and humid with the occassional rain shower (rainy season) while Central and Nothern Vietnam was dry (except Hue), hot but still a tiny bit humid. Average temperature was 30 degrees centigrade all the time, except in Dalat.
A friend of mine was there in January when it was dry and cool (20 to 25 degrees centigrade) in the North and hot and dry(ish) in the South.
If you intend to arrive in Hanoi and live from HCMC you should have least 3 weeks if you don't want to rush around too much. Anything less and you will spent more time on the bus/train/plane than actually spending time in places. If you have less time than you should - in my opinion - spend the time either in the North or South.
I was there in February/March and the weather was cool and fairly dry in Hanoi. Light warm clothing for most people would be fine, but you will see the locals wrapped in heavy warm clothing from head to toe!
We went north to Sapa (highly recommended) to see the terraced mountain sides and to meet the indigenous Vietnamese, and we were comfortable in a polar fleece.
Down south it is hot and humid all year round, but fairly dry in February/March. Definitely shorts and sandals weather.
Book early for Feb/Mar travel because it is around lunar new year when a lot of Vietnamese return to their families.
This is the best time to visit Vietnam. The weather is dry and cool everywhere in the country.
I assume you are from Scotland and from a part of the world where you know the difference between dry cold and wet cold. A damp 15C can feel a lot worse than a dry 5C. Similarly, a humid 35C is much different than a dry 35C.
The "North" (anywhere north of Da Nang) can feel very cold in December-January, and the south unbearably hot in July-August.
I come from a place where it can be quite cold (-30C last winter) but I never felt as cold here as I did in Hue in January.
If you take a look at the climate charts in any good travel guide on Vietnam, I am betting you will find no one ideal time to travel in both Hanoi, and Saigon, so I would suggest you decide what extremes of sun and humidity, and wet and cool you are comfortable with, what you hope to do, (eg. is Halong Bay on your itinerary?, or are you planning to do a walking tour of Saigon? are you bothered by monsoon rains?) and then make your careful choices from there.