Would suggest to use an international debit/credit card along with some cash separately.
get the currency exchanged at local registered forex shops instead of those available at the airports for better forex rate
I'll suggest you to start from Malaysia or Singapore as they are small country and You'll cover in very short period.After that you can go for Thailand or Vietnam. Both are very beautiful country and required lots of time to explore. If you are traveing to Vietnan then try to cover Cambodia too as they are neighbouring country and you can cover toghther. I've been to all South East countries and Vietnam and Philippines are my favourite one.
Indonesia - bali , Ubud , Gili Islands , Denpasar are best ones
Vietnam would be next (Hanoi nand Sa pa )
Laos is also the good one you can experience (vang vieng , pakse )