I don't know about the physical form - the physical form of life on earth is pretty diverse IMO.
But as far as the chemical form goes, my limited layman's understanding of why life is most likely to be carbon-based, is as follows.
The universe is mostly made up of hydrogen, helium, oxygen, and carbon/nitrogen. Other elements also feature, but those four are typically the most abundant. If there is any life at all in the universe, the likelihood is it will comprise of these common elements. Humans, for example, are mostly (96%!) hydrogen, oxygen, carbon and nitrogen (see https://en.wikipedia.org/wiki/Composition_of_the_human_body).
But what about helium! Helium is uninteresting because it is not very reactive, so the ways it can interact and "be stored and propagated as molecular data", as you very nicely put it, is quite limited.
Which brings us to carbon, which is quite reactive. It reacts with itself and gives you diamonds, graphite, buckyballs, graphene, nanotubes. It reacts with the most abundant chemical in the universe and gives you hydrocarbons. Sprinkle some nitrogen and oxygen in the mix - also very common elements - and you got yourself proteins and fats and carbohydrates and amino acids and whatnot.
So just based on that, it's more likely than not that life would be made up of hydrogen, oxygen, carbon and nitrogen, with carbon in the central role. That is not to say that there couldn't be silicon-based life, for instance, but it's just not as common an element as carbon.