If it's a new character you've made after playing the game at least once, then you should know better already.
Early-game stuff gets stored in your room at SGS. You'll be back to SGS from time to time, so you'll gradually sell this inventory down. It's also the inventory you'll use when trading with Blaine (and he's how you'll convert your otherwise useless-by-mid-game SGS credits into Charons).
Junkyard inventory goes in the trash bin next to the weapons vendor shop, for easy access.
World loot from the Underpassages gets carried back to Core City (because of the elevator) and stored in the barrel by the elevator on the Oligarch level. The other barrel holds stuff you'll be migrating to your house when you unlock it. Arena loot (and for me at least, other loot pulled from the encounters around Core City) goes in the three barrels by the weapons vendor shop right outside the Arena entrance.
Other loot stays in the nearest cities. Your call as to whether it's better to move the Ironheads loot to Core City or keep it to Rail Crossing/Foundry.
Now that you've got that system down, there's very little hauling back and forth. Sure, there'll still be a little bit, but you won't have to do twenty laps; just sort of consolidate stuff as you whittle down your various stashes.
All that said, I do think that for new players especially, it would be nice if you could pay someone (like, say, the Core City Housing people) to move your things from your room in SGS to your house in Core City.
