On a rainy weekend I basically wear some version of this with a mini skirt or skinny black jeans:
Sweater - Some variation of a comfy cardigan.
Skirt - A dark denim mini goes with everything. I also have corduroy and tweed versions.
Coat - A little tweed jacket like this goes with everything and can be packed into your purse without too much trouble.
Scarf - Extra chunky.
Bag - Purchased from Etsy a couple months ago. Despite a couple imperfections (a zipper that scratches my hands and the handles, no outside pocket) I've been really happy with this bag. I tie a leopard print scarf to the handle to tie the colors together.
Boots - I swear by my graphite Hunter boots (thanks Jean!). You can go miles around a rainy city in a pair of these.
Sunglasses - Because you never know when the sun will come back out.