wobs said:
There are a number of types of carbon, and organic life prefers a certain type.
Not quite! There are indeed different isotopes of carbon. About 99% of the stuff in our corner of the universe is carbon 12 which is stable. There is some carbon 13, which is also stable, and then there's the radioactive isotope carbon 14. This has a half-life of about 5000 years and it's made in the upper atmosphere.
Plants take in atmospheric CO2 and with it they get some carbon 14. It's not a preference; it just happens.

Organic material that lies underground for an extended period loses its carbon 14. The longer it lies there the more it loses. That's how carbon dating works.

Anything that was in the mantle before life evolved will be completely devoid of carbon 14.
We know of methane elsewhere in the solar system
There would have been lots of methane available as the solar system formed. Carbon and hydrogen are two of the commonest elements to be blasted out of dead stars. The others are helium, oxygen, silicon and iron. As the temperature falls and chemistry begins, hydrogen, carbon, silicon and iron all make a grab for the oxygen - but there isn't enough to go round.

It's no contest really; the silicon wins hands down leaving the others to scrabble for what's left. With the oxygen all taken up, carbon and hydrogen combine into methane.
The giant gas planets: Jupiter, Saturn, Uranus and Neptune, contain large amounts of methane. The inner planets were too hot and insufficiently massive to hold onto it.