Hey there. I did a similar trip, minus Tibet, in the opposite direction. I wish I could've gone to Tibet. On the Annapurna circuit I spoke to a few Chinese people who went to Nepal overland through Tibet -- it's spectacularly beautiful, according to them.
To answer your questions:
What is the best way (and cheapest
) to do this trajectory? From India to Nepal, bus from New Delhi?
There is indeed a long, express bus ride from Delhi to Kathmandu. There are also trains, from Delhi I know Varanasi's further but I would recommend going through there up to Gorakhpur to cross into Nepal. I came back to India the other way, the western side of Nepal via Banbassa -- it's very rarely visited by tourists, except those hopping over to Nepal for one day for their Indian visas. If I wasn't with a Nepali friend, I don't know how I would've been able to get out of Nepal. (Probably wouldn't).
Then from Nepal to Lhasa?
There are buses. You need a special visa to get to Lhasa, the ordinary Chinese one won't be enough; you also need a tour guide for this.
And finally from Lhasa to Thailand?
Burma is really difficult and expensive to get into, from what I recall; but what you can do is travel a bit in China and go to Yunnan province (right next to Tibet; in fact part of Yunnan was formerly part of Tibet). Yunnan is actually pretty gorgeous and well worth a visit. China's really neat. Very interesting contrast to India. You can get yourself into Thailand through the very southern part of Yunnan (the ethnic minorities there are actually ethnic Thai), which is called Xishuangbanna. This is just starting to become a popular backpacker area. The rest of Yunnan is very different from it, and has been attracting tons of lonely planeters for ages - it includes the ethnic Tibetan areas as well as the Jade Dragon Snow Mountains (the Tiger Leaping Gorge Trek is everything people crack it up to be) and some fifty other kinds of ethnic groups and beautiful villages and a few well-preserved old style towns, the likes of which are becoming more and more rare in China.
... Also, I'm particularly interested to go by train as much as possible during this trajectory. And I really don't mind cheap and dirty places, low cost travel, etc etc.
In India, trains are cheapest if you take the... what's it called, the non AC sleeper class. You need to reserve in advance; there are date limits; otherwise, there are sometimes "Foreigner" tickets on reserve. I think it was called foreigner, or tourist... something like that. Sometimes though, I took the bus, because I often couldn't get train tickets for where I was going.
In Nepal you can only get around by bus. I loved riding buses in Nepal. I was the only girl on the top of the buses but it's such an extra special thrill.
In China, both, but trains are far more convenient and they can also be really cheap. For trains you need to reserve in advance as well, they go on sale 10 days before. Actually I'm thinking about some of the buses I've taken - out in Yunnan, I don't know how you would take those if you can't speak Chinese. For trains the hard seat is ridiculously cheap, but it's also extremely crowded and everyone will be supremely uncomfortable. I had one American friend who ended up standing next to the toilet when she had a hard seat ticket; she was throwing up all 13 hrs of the ride. Aim for the hard sleeper. Keep in mind that it's customary for everyone to sit on the bottom bunk when it isn't time to sleep; the bottom's also slightly more expensive (by a dollar or something), and the top's the cheapest, but you have no room to sit up.
From Delhi to KTM I think -- I think -- the bus was 30 hrs. I think, I had a friend who took it and I think that's what she said. By train it's probably something like two and a half days.
The rest, I have no idea, but I would expect around 40 hrs from KTM to Lhasa, from Lhasa to Kunming in Yunnan, at least 20 hrs. From Kunming to Xishuangbanna I think it was like 15 hrs, and from there to Thailand I would guess at least another 10 hrs.
