What oil price will minimise new resource extraction? A higher oil price would increase incentives to develop new oil resource extraction, but it also increases the competitiveness of sustainable energy sources.

Conversely, a low oil price might mean less development of new resource extraction, putting projects such as hydraulic fracturing or offshore Arctic drilling on hold.

What I wonder is: what oil price will lead to the lowest level of new resource extraction?  Or, in other words: suppose that I strongly oppose the development of new resource extraction with potentially very high environmental costs (such as hydraulic fracturing or Arctic offshore drilling), should I be glad when oil prices or low... or when they are high?
An oil price of 0 will make any extraction of oil unprofitable and hence imply no further oil extraction.

You should think about how prices carry signals. A low oil price (even if not 0) carries the signal that we, as society, do not value that oil as much. The conclusion is imminent.