For a two month trip I would recommend renting and getting the bus or train between towns. You cannot take a foreign bike in Vietnam but can hire one there although it is apparently illegal, take advice from other travellers who know the current situation.
The best bike will be the Honda wave 125, great machine, any Japanese bike will do and avoid Chinese, Minsk will probably not be available to rent and only a few left in Vietnam to buy, a bit unreliable on a two month trip.
If taking public transport there are no problems at borders, I think Vietnam is the only place you must get a visa in advance in Laos or BKK, others might know different.
Don't miss the usual tourist spots, Luang Prabang in Laos, Halong bay and Hue in Vietnam, Angkor wat in Cambodia, all full of tourists but worth a visit all the same.
I have forgotten how much bike hire is, about 5 quid a day from what I remember. Take your own helmet, summer gloves and a well ventilated, lightweight jacket.
Remember ordinary travel insurance only covers you up to 125cc so don't be tempted to hire bigger unless you are covered.
International driving licence might be useful.
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