The major decision with cycle touring is whether or not to to take camping gear. Tents and sleeping bags add a lot of weight but give much more flexibility with route planning, and make the trip much cheaper! For long distance tours we've taken 4 panniers on the bike, sounds a lot, but you soon forget (after 2 weeks), and it's great being totally independent. For South East Asia, everything is cheap, accommodation widespread and you need few clothes in the heat. Pack light and take 2 bicycle panniers of gear. There's lots of roadside stalls for drink stops, but be careful not to weigh yourselves down with too much sun cream.
You'll need the right tools and spares to cope with bike problems - anything from a puncture to a broken spoke or chain. Make sure your bike has reliable components, it's hard to find a 9-speed chain between Hanoi and Saigon. Anyway, some of the best experiences happen when you have to sought out problems.
Part of the reason for going on a bicycle tour should be to get away from the complexities of the world. Having to struggle a little bit creates a better challenge, and a humble camping site close to the earth and visited by God's creatures is sweeter than the finest hotel. However, carrying the proper gear can make a real difference. While a little hardship just increases the challenge, suffering from rain, cold, insect bites, hunger, lack of sleep, sunburn, frequent flats, broken equipment, getting lost, and dangers on the roads can be alleviated, if not prevented, through careful selection ahead of time. The real solution then is not to carry a little equipment or a lot of equipment, but to carry the right equipment.