Best Place To Go For Budget Travel In Asia

Answer :
Well they all have their good points and each one is definitely worth a visit. I'm sure you won't be disappointed whichever one you choose and you haven't even thought about Cambodia-might be worth thinking about. Lets stick to the three you mentioned though.

Thailand's got the best beaches if that's your thing but to my taste buds the worst local beer although Black Tiger when it was around was a fine drink. The contrast between the city of Bangkok and the rest of the country is huge.
Vietnam's probably got the most varied geography and good beaches but the food isn't up to scratch compared to Thailand's. The food isn't bad, it's just not as good as Thailand's and to be fair, not many countries' food is, except for maybe England's. Superb coffee and bread however thanks to our French friends.

Laos is the most laid back / backward. It is cheap as anything with beautiful scenery and has probably the best beer of the three although some of Vietnam's beer runs a close second. Good coffee and bread.

I'd pick Thailand for its combination of great beaches, unique culture, cheapness and great food. Just beware that many people make the same choice! I have to say though that I'm finding the Vietnamese people more genuine generally and I haven't really spent enough time in Laos (couple of weeks) to really get a feel for the place but the people seemed nice and it was pretty easy to stray from the beaten track (if that's a plus.)