Probably the simplest and cheapest means of transportation of asteroidal resources will be by a simple steam rocket. This uses plain water as the propellant, and a solar or nuclear heat source, e.g., a large foil mirror array to create a super hot chamber to introduce the water into.
Water is probably the most abundant volatile in most volatile rich asteroids near Earth.
The steam rocket is lightweight, as is the equipment required to extract and store the water from the asteroid. All we need is an oven to extract the volatiles from the asteroidal material by simple heating and piping. Unlike other rocket fuels, we don't need to further chemically process the resources. This saves costs on equipment launch. Lower risk for fuel extraction and production because extracting simple water for fuel propellant allows a much simpler design than producing alternative fuel propellants.