A trend I’ve seen a lot is for the player who wins priority to choose the secure crisis. There might be reasons behind that, but I’d like to advance a line of thought that choosing the extract may be the right choice.
Scenarios are generally symmetrical, but not all symmetries are equal. Notably Spider Infected and Cube Fragments have a central grab-able asset token. By knowing you have priority, you can send out a character to grab the central asset as you first activation. That will typically gives you at least a 1 VP lead over your opponent.
1 VP might not sound like much, but it means you are dictating play: your opponent has to come to you to overturn that lead, else you continue to out-score then every turn. Dictating terms to you opponent can really help you, especially if you have built your team with that in mind.
They will have leave 1-2 characters deep to score their own secures. Let them come to you and use your threat advantage and activation advantage weigh in your favour.
Including ways to keep your early gambit safer, like bodyguard, rerolls donors or out of activation moves or places help protect your investment. Forcing them to split their force or suffer a serious VP deficit early on is the plan.
By choosing an extract with a central asset, you can make them play the kind of game you want, and take an early lead that puts them on the back foot, both in terms of field position and victory track.
With that in mind, if you don’t have priority and are given extract to choose, it might be an idea to avoid centrally placed Assest crises.