Consulting one's Network: When in the Process?

Hello all,

when chasing a career opportunity, when's the right time in the process to reach out to one's network for background information?

This is a specific situation. I am currently pursuing internal transfer opportunities within the business I work for, and have been identified by a recruiter as a potential candidate for a position posted. While I have some doubts about the position as described, it might turn out that this is an interesting opportunity. I have contacts in my network, both inside the company as well as outside the company, that could be very helpful to provide information on the context of the target role. I'm especially interested to work in a growth environment, but have little insight into the business model of the division in question here; I'm expecting my network to be very valuable to judge the potential of this opportunity when it materializes.

But: When is the right time to reach out to these people? Right away, to help me judge whether this is an opportunity that's worth pursuing before I invest too much thought? Or should I better wait until after a first phonescreen/interview, so that I have a better idea on what the requirements are and whether I see myself "fit"? Or would you rather wait until the very end, when an offer is on the table, and then probe the network to support a go/nogo decision? Do you think it's smart to involve people along the steps of the way, continually, repeatedly?

Thoughts would be appreciated. Thanks
Jochen