Data on the composition and orbits of asteroids I am interested in the composition of asteroids from the perspective of determining potential targets for mining.

I expect there already exists some data that can be used to identify reasonable targets for mining.

The specific mining method I am looking to evaluate is to send a "collector" out and "grab" a target, bringing it back into LEO for mineral extraction.  Because of this I would like to identify targets that are &lt; 20m diameter. The ideal material to mine/extract would be a precious metal of some kind. This would give the most "bang for the buck". (The buck in this case being the effort rather than Delta V).
Considering the ideal material, I suspect a list of "M" type asteroids and their properties would be the data I am after.

I saw a question that asked about using IR Spectroscopy to determine the surface composition of asteroids.  That gave some good insight - but no indication of where such data currently exists. A table of this data would be a reasonable starting point.  

I am also wondering if we can determine anything about the relative density of an asteroid by the gravity it exerts on nearby objects.  If that data is available anywhere that would also be an interesting place for me to look.

I am also interested in trying to determine the orbits of any target asteroids, so where would I look for data on the orbits of those that are selected?
The JPL Small-Body Database Search Engine is a good place to start.
If diameter &lt; 20 m, then probably absolute magnitude H > 25.
Fortunately we know of over 4000 asteroids in that size range, mostly after close approaches to Earth.
Unfortunately the orbit and magnitude are all we know about most of those, due to limited observational data.
JPL SBDB lists only about 40 asteroids with known Tholen spectral type M, all with perihelion q > 1.5 AU and diameter > 30 km.
The picture is a little brighter for type S, with over 300 known, a few with diameter &lt; 2 km and minimum orbit intersection distance &lt; 50 LD.