BEST TIME TO TRAVEL TO TAIWAN??

Please advice me the season i should travel to that island. I need to know is better to visit during autumn or spring?? i wish to visit during the season whereby the weather is soothing and breezy. not hot nor too cold. i am also trying to avoid rainy seasons. Some suggesting to go end of april until may.. some end of sept til early oct.. so need more advices what will i be able to check out if im going during these period of time.. thank you!