I am a new player (Level 3 and only a couple hours in) and I personally don't care to beg for pets or resources as I feel that earning them is the best way to learn a game like this. I, instead, would like any experienced players to leave a tip or two of things they had wish they knew. Thanks so much!

you can adopt from the pound 

If you breed a critter with a red star,the offspring does not retain the red star.

You can stack schemes and blueprints for items and buildings to make them cheaper. Except for the Golems.