Start Boosts give you a rocket pack and a handy head-start on a level - these cost 50 gems though. If you want to get even further ahead at the start of a level, you can use the Super and Mega Head-Starts for 100 or 200 gems respectively.
As for power-ups as you work your way through the game, you'll be able to access power-ups through Artifacts. The Ant Repellant and Spider Repellant (200 and 100 gems, respectively) are great at keeping those particular foes at bay, although you will pick these up during the course of play too. The Dodo Stopper costs 50 Gems, but the other two should be your priority.