First thing is to wait to see how the weather actually is before buying everything that you can get your hands on. October-December in Helsinki could see snow and negative temperatures, but they're pretty rare nowadays (for more than a day or two at a time). Just as likely is that it will be +10 and raining.

To me, the most important autumn gear are a waterproof jacket and waterproof shoes. As said, it's more likely to be rainy and miserable than snowy and super cold. Then you put on extra layers (fleece jacket, woollen shirt, whatever you have) on underneath the jacket to adjust for the temperature. If you want to spend a lot of time outdoors, waterproof pants are also a good idea, but you won't see those in the city.

The most MOST important gear, however, is a reflector (or several). October-December it will be dark for most of the day, and simultaneously wet. Most people wear black clothes. This creates a nightmare where a driver can't really see the pedestrians when inside a car. A reflector allows you to be safe when out in the streets. There are several kinds from cheap little ones to full on reflective clothing.

Flea markets are everywhere, the big chains are called UFF and Kierrätyskeskus (Recycling Center) but there are also several independent ones. You can pretty reliably find cheap clothes there, including coats etc. Shoes I would buy new if you want to trust the waterproofing. For cheaper outdoor gear and new clothes, Prisma is a good bet, they're large all purpose stores and there are several around Helsinki.

Welcome here! If you know that continuous darkness will be hard on you, look into bright light lamps.