Custom road bike

[KnottedYet]

I've only ridden all-carbon once. so I really have no basis to speak. (Except to say I didn't like it, but it could've been the geometry, not the carbon)

[Mimosa]

The biggest advantage of carbon is the weight ... that's more or less it.
Steel, Ti and/or alu frames have more strength as a whole. Meaning if you would drop your bike chances are more likely a steel bike would show only paint scratches and carbon could have serious damage to the carbon. Carbon is only strong is the direction it was designed to be and steel (alu) is strong as a whole.

Imho it would be wiser for your first bike to go for steel, ti or alu frames.