Hi,
A couple of years ago, as part of a longer trip I spent three weeks between Thailand and Laos.
Briefly, spent a day or so in Bangkok. Got an overnight train to Nong Khai on the Thail/Laotian border. Spent two nights there before going on to Vientiane.
From there I spent a couple of days in Vang Vieng (spectacular karst mountains, river swimming, cave trips) before going on to Luang Prabang (atmospheric colonial town - world heritage site).
From here I went up river to Nong Khiaw and then on to Luang Namtha in northern Laos.
After some time in Luang Namtha (great for hiking) I spent two days travelling down river to a more northern part of the Laos Thai border. (Huay Xai)
A couple of days were then spent in north Thailand before another train from Chang Mai back to BKK for an onward flight.
While sparse on details if you look at these destinations on a map you'll get an indication of the areas involved. All travel was overland - between trains, boats, buses and chicken wagons it was a brilliant and memorable trip. Internal flights are cheap though if you did want to fly. I believe internal flights in Laos are not recommended for those without parachutes/ nerves of steel.
Can't speak for Cambodia of Vietnam but Laos is an absolutely amazing country to visit with lovely people, fanstastic scenery and a glimps of how little some people in the world live with.
Final note is that many people do this trip somewhat in reverse, travelling to Northern Thailand first, then to Huay Xai. From there you can get a two day boat down the Mekong to Luang prabang, and on to Vang Vieng etc. That's 'the circuit'.
Final final note - you can see a lot in three weeks, but in Laos and Cambodia at least the travelling can take all day long. Its great, but can be grueling.
Enjoy, I'd go back in a heartbeat and would love to take in southern Laos next time.