at the beginning dig everything. at some point concentrate on uncommons.
I've been considering if this is actually beneficial vs targeting the 100% Common dig sites, b/c they are so much faster.
NOTE: Just added this line after writing this note. I realized my times listed here are with the CW 20% dig speed bonus active ... so just add 20% to all the times for a non-buffed dig time analysis, but the ratios will hold the same.
The ones with Uncommon %'s take 3x-5x as long (depends on Uncommon %), and 1/2 the time you still end up with Common. It might actually just be "quicker"/more artifacts of value earned in the same amount of time if you go for all Common. Get 3-5 Common in the time it takes to get 1 chance at an Uncommon.
So in 120 hrs of digging, either get:
[a] 20 Common = 1 Common every 6 hrs, or
(likely) get 3 Uncommon & 3 Common (50% rate) = average 1 Common every 6.7 hrs
So focusing on Common is slightly better (~12% faster), but can really be considered about even as far as raw value goes, probably more likely to come down to how well you micro your digging vs doing long ones, walking away and letting it finish.
However . . . getting more artifacts could be beneficial, b/c this means you have more types in your inventory which means you have better selection of what to keep, what to upgrade, what to use as fodder. If you already have your best pics, then it doesn't make a difference.
I didn't consider the cost of the digs, though. The dig times seem related to % chances of each level, but cost seems unrelated to levels but instead related to order of encountering within the map, so early map digs are cheap, late ones are expensive. So I suppose it comes down to money ... if you have tons of money, nothing changes, Common is slightly more efficient. But if all the later digs are equally expensive, and you are short on money, then using it on the Uncommon digs could make more sense.