NASA is seeking proposals from
advanced concept research studies in order to help make ambitions into
reality in regards to the agency's ambitious asteroid capture mission. The
general plan: launch a satellite into space and use it to capture an
asteroid, which then could be brought into lunar orbit in order for
up-close study and exploration training purposes.
http://www.examiner.com/article/nasa-seeking-ideas-to-make-asteroid-capture-mission-a-reality

1, Spin: as little as possible.
2, Orbit: as similar to Earth's as possible. The less Delta V involved the better.
3, Mass: start small, 30 meters or less.
4, Composision: solid no rubble piles, ice or rock ok.
5, Speed: Delta V again.
6, Posistion: important for both sending craft and drifting it into the L1 slot.
The easiest way I see of doing it is to send up a nuke powered ion drive and rock grinder. Mass is mass. powdered and ionized rock will do the job just fine. Vectored thrust and autopilot for when things get of track.
This won't be fast but it will get the job done.