I recommend traveling Thailand by train or by plane. Buses may be faster than the train, but your personal movement is more restricted, and you have to deal with traffic when entering and leaving cities.
There is a train line that runs all the way from Chiang Mai through Bangkok and down to Malaysia before ending in Singapore. You can take the overnight train to avoid spending money on accommodations, but then you miss out on all the beautiful scenery. Seat 61 has everything you know about train travel in Thailand.
I booked my travel in advance from the USA with 12go.asia. They charge you a pretty steep fee, and I only recommend using them if you have to travel on a certain date and you aren’t going to be anywhere near a Thai train station before your travel date. Otherwise, you can purchase for much cheaper and get more options at the station. Keep in mind that sleeper cars should be booked at least 2 days in advance during peak season.
Budget airlines, like AirAsia, offer fares that are often the same price as taking the train, so if you’re more interested in the destination than the journey, that is the better option for saving travel time.
Buses, as I mentioned, are subject to traffic, and often times, you are crammed in a mini bus instead of a motorcoach. I find that to be the least comfortable way to travel, and it often costs the most. Another down side of buses are that, in bigger cities, the stations tend to be located away from the city center, and you end up having to pay for a taxi to get you to your ultimate destination. More often than not, trains terminate in the city center.