Should I book Thailand Rail tickets online (pre-trip) or at the station when I arrive?

I tried to use the train, but i found the rail system a bit limited and couldn't use it (from Bangkok towards south) so i ended up using the bus instead. Unless you go on a public holiday you don't need to book anything ahead. You can get around by bus if you book one or 2 days in advance, and all those "Travel agencies" near hotels or tourist destinations will be happy to sell you a bus ticket to pretty much any city.

I took the bus from Phuket to Singapore, and since it was only ~USD 50 and i didn't have a detailed map of that area I expected it to be not more than maybe a 5h/300km bus ride. Little did i know...

A word of advice: Don't be tall if you use the bus - the legroom is worse than in economy class, even in what they call "luxury coaches"! The bus will have a stop every few hours so you can get food and use the public (squat) toilets. Bring your own paper and be prepared for waiting in queues! Also, those stops are rather short (10-15 mins), so if you take the waiting in the queue into account then it's quite often either food OR restroom break.

To be honest, for the shorter rail journeys such as Bangkok to Chiang Mai, you don't need to book beforehand. Between Bangkok to Phuket you should know that there's no direct rail line; rather, there's a train to Surat Thani and then from there you have to travel by bus / minibus. For the overnight sleeper trains, as Peter mentions in his answer, you may want to book tickets a couple of days in advance once you reach Thailand as these tend to be popular among travellers who want to save a bit on accommodation for a night. (There are a couple of overnight trains from Bangkok to Chiang Mai which are popular ones.)

It's not that hard to book tickets at the station in when in Thailand, as long as you are willing to be a bit patient with rail officials who don't speak English (and there are many who don't). You will usually find some official or police officer or the other who can direct you to what counter to book your tickets at - sometimes, you need to book at different ticket counters depending on your destination.

Trains do get fully booked around holidays such as Songkran but that's celebrated in April. If I remember correctly from your previous questions you're travelling in February / March (?), so this should not be a problem for you.