do event route matter?

It doesn't matter. And whichever route is fastest/easiest heavily depends on what CEs you do have and what resources you have on hand.

Regardless the walkthrough does list which option is generally the fastest.

It doesn't matter. The routes you choose is up to you. If you want, just pick the routes with the most bonus. Most of my servants have bonus on stones, so i'm going with the stone route.

For most efficient method, go for the wood path. Should be 1-A, 2-A, 3-A, 4-C, 5-A, 6-A, 7-B, 8-A, 9-A, 10-A, 11-A, 12-A, 13-B, 14-A, and any of the three for 15. This way you will get through the development quest the quickest so you can open the higher level free quest to farm, which is way more efficient. Also, wood get bonus from 3 star CE, which is the easiest to get. Raikou would be the best to use since she has a bonus on getting wood.