I typically carry a huge amount of storage on me (at least 300), which sucks for encumbrance but if you use the double-back looting tactic, it doesn’t much matter.
Ie:
Build a fast, lightweight, efficient vehicle that can dip through traffic and avoid taking damage. It only has to be able to survive until evening. Drive it away from your mobile base and map out everything along the way. Don’t stop unless absolutely necessary (ie. the engine falls off).
When evening falls, hop out, note it on your map, and walk back in the dark to your mobile fortress, looting everything interesting on the way. Priority importance is gun shops, antique shops, museums, science labs, bunkers (I typically loot these ASAP and store it in the buggy for later use), and anything else you have room for. Try to avoid combat, but a silenced gun can take out just about anything in the dark even with enormous encumbrance. Avoid walking into flashing squad car lights or headlights that are still running.
When you get back to your fortress and are flush with loot, dump it all in the cargo hold and drive your behemoth to where you left your buggy. Get back in the buggy with an empty inventory, rinse and repeat.