Our recommendation is to turn on "Google flight tracker" this will send you updates based on pricing trends and deals. Pro tip: use a private browser and buy your flight on a Tuesday (they're usually the cheapest)
We recommend to stay in Letojanni itself. If you stay at the top of the mountain in Taormina, you will have to book car services.
Taormina is about a 15 minute ride up the mountain, you will need a car/car service, ride to the cable cars, or a bus to get to the top. That being said we absolutely recommend taking time to visit the beautiful city!