How much gain is needed in a Phono Preamp for a 0.2 to 0.3mv low output moving coil?

Lots of good comments, many of them cautiously worded...I hope your takeaway is that you could do better.
I have recently troubleshooted a friend's Chinook/Prime setup and before we got things sorted out had to get replacement tubes for the Manley and properly functioning junction box from VPI. Even after working through that, with his Ortofon Qunitet Black(0.3mv) his Primaluna linestage needed to be cranked up very high and while generally musical, I wouldn't call it a quiet presentation, nor one that I could live with. IMHO, 60db gain in the phono stage would be better matched with a cart >=.5mv. There are plenty of nice phono stages that offer 65 or 70db gain. When dealing with small phono signals an extra 5db of quiet gain is nothing to sneeze at.
Contrary to some here, I would suggest staying away from adding a SUT at this level of system, as most of them will take away from the purity of the signal, add more cabling and related susceptibility to incremental RFI/EMI. When considering adding a Kondo SUT to your 6figure table setup, then maybe you can convince me otherwise. Cheers,
Spencer

Lots of good suggestions in the last day or two here. 
I agree with the brief comment that a solid state phono stage will give you a lot higher chance of quick success. It hasn't been discussed much in this thread(but plenty elsewhere!) that low level phono signals are most susceptible to picking up RFI(ie. radio)/EMI noise. Tube phono more so. Go with a ss phono stage with plenty of gain and you will high probability of quick success without headaches.
The Art9 sounds lovely and balanced, great with classical, perhaps a bit on the sterile, detailed, cool side vs. Dynavectors which also are frequently mated with VPI arms and tend toward warmer, punchier, more relaxed sonic profile that appeals to many. Either is a great choice. Cheers,
Spencer