We don’t see the rebel fleet in action until Jedi, and it does seem to be carrier-heavy.
As for the independently-operating fighters: they have to land somewhere, the pilots can’t just live in them and they need to fuel, receive maintenance, and re-arm. That’s either planetary (or equivalent) bases, or carriers, much like pacific WWII air operations were a mix of island airstrips and carriers (lots, and lots, of carriers).
That’s all for the original trilogy. What we have in addition, however, is a limited look at the inter-trilogy insurgencies and nascent rebel alliance, in a variety of movies and TV shows (e.g. Rebels). Those do seem fairly heavy on carriers, from what we get to see, plus light gunships.
I definitely remember gunships and troop transports, but my memory is just failing me when I try to think of carriers. I guess this is left over in the legends canon now, but much of the rebellion's fleet having been repurposed from civilian transports/cruise liners also serves as a good explanation as to why they wouldn't have many carriers as well.
[edit] though, I do think that line of argument’s a bit weak. I could see going either way on the question of whether the Mon Cals slot better into the “fast carrier” paradigm or are better regarded as filling the role of heavy cruisers or battlecruisers. Not a lot of Star Wars ship designs slot quite so clearly into a fast carrier designation as the Republic’s primary Clone Wars warships.
While the Empire can afford to throw away pilots, the Rebels need to give their pilots every chance to escape from a failed battle.
To be fair Luke did "bullseye womprats in his T16", and his friend and rebel pilot Biggs could've vouched for him.
My impression was that Luke's X-Wing was his reward for saving Leia - in the same scene we see Han leave the Rebels while carrying a sizeable amount of money.