Belaclya Always do the Free Events. Always. If you aren't going to have enough Energy to finish them and you are fairly certain of it, then pick your way through them. Do this by
1) Clearing the tiles that lead to the tiles or things you need to finish each quest you are given, so you can go onto the next Location
2) Clearing the tiles that lead to the Special Item (the one used to purchase Equipment for that Event)
3) Clearing tiles that lead to XP boxes and Treasure chests
4) Clearing tiles that lead to Materials boxes (those cubed boxes)
5) Clearing the tiles that lead to Coin and Material tiles
The order these are numbered is the order you should prioritise how you would clear the tiles. Finishing a quest takes you to the next location, so that is most important. Getting the Special Item to buy Equipment is next what matters most, since that is basically the reason for doing the Event. The Treasure chests and XP boxes cost you no Energy to break while giving you something, so those matter most next. The Materials boxes give you items at a low cost to break them, so they come next. Last come the Coins and Materials tiles since they cost the most overall Energy.
When breaking tiles to clear a path to only the tiles you want or to the place you want to go in a location, you should then try to clear the straightest path while also trying to clear the lowest value tiles you can. You should also keep in mind all of the tiles in that list you will want to try for, and clear your path in such a way to make it easier to get to the later ones while going for the first ones if you can. Basically, you want to avoid using Energy as much as possible to unnecessarily to break unwanted tiles.
The reason to always do the Free Events is that the Main Game is always going to be there, but the Free Events are only there for a limited time. So you should get what you can from them while you have the opportunity AND while they are free. Also, if you have two Free Events you are playing at the same time but won't have the Energy to complete both (or to get everything you might want from both), then concentrate more on the one that has the better Equipment you can purchase with the Special Items in it. There are exceptions to this strategy, so use your own discretion.
Hope this is helpful.