So far there is only progress for two of the "big three" - the Federation and the Empire - and the benefits are limited. Building rep with the Alliance doesn't give a rank increase or an associated benefit. This may change when the "Powerplay" update happens, we don't know.
You can build rep with all the factions with no downside, ie ranking up with the Feds doesn't make the Empire hate you.
Yes, the population is spread thinly - it's the nature of a game based in such an enormous sandbox.