Actually, SE only recently modified the gathering buttons for collectables, so that really isn't any particular "rotation" you need...
Basically, there isn't really any rotation at all anymore now. They have made gathering "easier".

If you look at ANY Collectable Appraiser NPC,

you can see the required collectability for submission. And so you just need to hit that amount base on your stats.

On the collectable gathering panel, you have 3 basic appraisal actions to increase collectability: Scour, Brazen and Meticulous. Please just read the tool tips to see what they do.
And you have 1 buff action to increase the power of any appraisal action: Scrutiny.
So usually you wanna hit Scutiny and then hit Meticulous, as it has a small chance of not decreasing the node's integrity. But it really comes down to your stats, and the collectability that you're aiming for. We don't know how much collectability you'll get from appraisal actions, which is dictated by your current perception stats. We also don't know how many Solid Reason / Ageless Words (300 GP) (NOT on the collectable panel, but together with your other regular actions) you can use to restore integrity. So you have to determine that yourself.

Although, I'd suggest you NOT to bother too much with scrips until level 70-ish. As you can see from the picture above. The amount of yellow scrip you get is much higher than that from a level 50.