Which travel period will be better?

Hi there I am planning a 10days Taiwan Trip
The places I will be visiting
Day 1: Taipei > Taichung
Day 2: Alishan
Day 3 and 4: cingjing farm, nantou
Day 5: taroko gorge, Hualien
Day 6-10: Taipei - yang Ming Shan, fisherman wharf, shifen/pingxi, Ximending
Kindly advises which traveling period would be better
Option 1: 24 Sep 16 to 03 Oct 16
Option 2: 01 Oct 16 to 10 Oct 16
Option 3: 22 Oct 16 to 31 Oct 16