The Animal Speech power and a megasloth works pretty well for early vault looting. Otherwise maybe the super strength power could help haul a little more aswell. Pretty hard pressed early game to go vault looting otherwise without powers or pack animals. Best to just wait til you have animals or a forced labour force first before hacking that transmitter.

Have you tried SRTS Expanded?

Transport pods are probably the easiest way. Most vaults (at least the sealed ones, don't know about looted) will tend to have plenty of stuff you can deconstruct for steel and components, and they usually have those huge tanks of chemfuel too.

pods+biofuel refinery

Trees are generally abundant in most biomes, along with Vaults being steel and component rich.
Trees>fuel
Vault decor>steel+components.