I know the Muslims are trying to get a toehold here--so is the army on the side of the Buddhists or the Muslims?
Buddhists
It's amazing how many people jump straight to wondering if Muslims are involved.
Thailand's Muslim population is relatively small and isolated. They're certainly capable of carrying out terrorist attacks, but they're nowhere near the capability to take over a city hall, let alone the national government.
The split in Thailand is, in large part, urban/rural. Thaksin has never been very popular in Bangkok, but he's beloved in the countryside. He's a telecommunications billionaire, the richest man in Thailand, and there have been persistent claims that he's used the government to make his family even richer.
As to who's side the army's on, Thaksin's or the opposition's, that remains to be seen. There's evidence of a split within the army, and the tanks outside the government house are apparently tied to the opposition, but that's not clear.
The most hopeful sign is that the leaders of the coup hastened to pledge allegiance to the king. He's the most stabilizing force in the country, but the flip side is that he remains revered in part because he only rarely gets involved in politics. I don't see any way he'd choose a side, but he could try to keep everyone calm (which they appear to be) and call for elections soon.