Achenar is a somewhat disappointing system, for people who are not True Believers in the Empire. The star is a hot B-type star - which means the habitable zone, and therefore the Earth-like planets and most of the space stations, are quite remote from the Arrival point. 21,000 Ls away, to be more precise, which is a good five minutes away in Supercruise. The nearest station is 2336 Ls away. If you are a True Believer, or want to become one, then there's lots of Tourist Beacons in Achenar to visit and scan, that give the lore and backstory.
Achenar 3 is a landable high-gravity planet (6.73 G) so for Horizons owners, it's a great place to practice high-G landings without risking your ship thousands of LYs away from inhabited space. But since you don't have Horizons yet, this is currently irrelevant to you.
All the factions in Achenar are Imperial-aligned, so every mission you accomplish there will boost your Imperial rank and reputation, and once you become Friendly or better with them, it can give opportunity for lots of valuable rank-earning missions. However, all the missions will be one-way rather than loops (unless you create the loops yourself by accepting lots of fetch-and-return missions), because no-one outside a permit-locked system ever offers missions to go into a permit-locked system. Two of the Achenar-based factions have presence outside of Achenar, plus there's one faction based in Condovichs that expanded into Achenar before the "no expansions or retreats in Capital systems" rule came into effect. For those who don't yet have the Achenar permit, you might want to consider going to Cemiess, Taevisa, Condovichs and Liabeze to do some "pre-loading" of rep with the Achenar factions.
Cemiess and Condivichs are, personal opinion, just as good if not better places to work up Imp rank. The Cemiess-Vequess loop was quite popular back in my day, as those two planets tend to often send missions to each other.
Personally, I've been to Achenar 10 times (according to the EDD visit-counter), but only once since 2016. I'm Allied with two of the factions, Friendly with Condivichs and Cordial with the other three.
