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.
All we need is an oven to extract the volatiles from the asteroidal material by simple heating and piping. Unlike rocket fuel, we don't need to further chemically process the resources. This saves costs on equipment launch, allows a simpler design, and reduces risk for equipment failure. The rocket becomes simpler and more reliable. A simple thermal heat chamber is used instead of combustion apparatus for chemical rockets or the electric power plant and grids for electric ion drive.