Well, that all kinda depends. What kind of frigate?
Duripant, Ours (if your computer doesn't lag) or Renyn are nice and safe for mining. I run combat missions for a living, though, so I'm not the best guy to ask.
Bantam, or if you can get one, an osprey with Miner II's is the best mining ship short of a BS or barge, but its not good for much else, so dont waste money on it too early...