I agree with the above, comets are great. They tend to have a lot of a lot of things.
As for asteroid miners, I suggest them for two reasons: it teaches you to make functional ships and support ships, and you can use your shipyards to produce mines. Relying on industry alone for increasing mining capacity can sometimes lead to tears.
Usually people run out of Duranium first. If you're aggressively building mines, you'll be seeing pain in corundium.