Storage is on a per planet basis. So if you have storage on Ancyra, you have to pay separately for storage on Jangala in Corvus. And you have to fly to your stuff. No shared inventory between planets.
However, I will point out there is an abandoned station in orbit of Asharu in Corvus, which has free storage (and a free transport ship), that doesn't cost an upkeep fee. You can dump as much stuff as you want there and it will never cost anything. There's a couple other abandoned stations scattered around where you can do something similar, but I find Corvus centrally located enough.
Personally, I'm a weapon packrat, and until I've got my own colonies (which also provide free storage without a fee), I typically store every weapon I find there, as well as stash ships there when I don't need them. For example when trying to be stealthy for some missions, or going out on deep space exploration missions and don't want to drag along a capital. Since weapon spawning is RNG, I like having my options. In fact, if I see good rare weapons, but don't have ships for them yet, I'll buy them and dump them in that station as well.
