The answer is going to depend on your exact itinerary, but my sneaky suspicion is that hubbing out of Kuala Lumpur and flying Air Asia everywhere would be the cheapest way to do it. Not only is Air Asia cheap and ubiquitous, but the passenger taxes & charges at KUL are noticeably lower than in SIN.
That said, Kuala Lumpur's LCC terminal is a bit of a hole and looping through can be slow, so if there's a sensibly priced alternative I'd willingly pay some money to avoid it. (The long-delayed new terminal is scheduled to open May 2014, but I'm not holding my breath.)
Also, there are definitely some legs of the journey you'll want to fly direct, or even consider crossing overland. Domestic Indonesian flights (eg. Jakarta-Bali) are ridiculously cheap, and Bangkok-Laos-Cambodia-Vietnam can be done overland cheaply and reasonably comfortably. Train is also a serious alternative for all travel in China, including HK-Shanghai.