Hi, that's fine, everyone would be much excited when doing their first trip! At that time in Taiwan it won't be cold, I think if the weather is fine you can wear summer clothes, but don't forget to bring coat and T-shirt in case it rains. October seems not typhoon season but it is really hard to predict, just bring enough clothes and come, I think no matter it's rainy or sunny, you'll have your best Taiwan trip! BTW, Welcome to Taiwan.

Thanks Mrs Mia. :)
Shopping for summer clothes during that period is fine right?

Yes, you could purchase summer clothes, but not as reasonable as the price in July and August.