Looking for Winter gear (Commute via Bike, Mild Winters)

So I recently got into this community and as Winter is slowly approaching I am looking to buy and keep following items for quite some time:

• a jacket: should keep me warm enough to around -5°C but as I cycle my commute should keep be too warm on its own, it does rain a lot (snows less often) so that should be kept in mind as well

• a pair of shoes that fit the same criteria mentioned for the jacket.

Also, my budget for both items is not too high (~100€) per product.

If this does not fit any rules for posting, please tell me so & if this is the wrong Subreddit tell me too :)