What is the weather like for the beginning of October?
I can report that it was very similar to the weather in New England in September. You need layers because it may be cool and crisp in the morning, warm in the afternoon, and cold in the evening.
I'd suggest
pants,
a t shirt,
a lightweight long sleeve shirt (like a Columbia button up shirt, those are pretty lightweight and dry easily if you sink-wash them),
a light sweater (it doesn't have to be pure merino wool like all the youtube traveler influencers want you to buy- if you have something that is light knit and a blend of fibers like wool/synthetics or cotton/synthetics, that could be just fine),
a light packable rain jacket for extra warmth/staying dry if it rains, and
a snazzy scarf.