I commute on the bike rain or shine, and in Portland OR it is raining and/or chilly most all winter. I wear:
- A waterproof biking jacket. I have a Burley, no longer made, but Showers Pass looks nice too. $100-150. Something not "bike-specific" could be less, but you do want the arm pit zips and vented back.
- A fleece layer under the jacket.
- Rain pants. $80-ish. Bicycling ones are nice but not necessary. Carry in bag if not needed.
- Waterproof booties for your shoes, they wrap and velcro around the heel. $25.
- Waterproof, warm gloves. $45.
- A baseball cap under my helmet keeps my head dry enough. A thin balaclava for cold days.

We don't usually have snow or ice or many sub-freezing days here, so those clothes work fine. I excuse myself from riding if it is snowy/icy, because I don't have studded tires.

You can control how much you sweat by how hard you ride. If you're in shape and the ride isn't steep, you can usually find a pace at which you don't sweat much.

At work, it's nice to have a place for your stuff to dry out during the day. Ditto locking the bike out of the rain.

Fenders are a must. Unless you want to be covered in a fine spray of dirty water.

As are lights - I have headlight/taillight on the bike as well as on my helmet, plus a really bright headlight on the bike - and as much bright color and reflective stuff as you can stick, sew, or wear on your clothes and bike. On a dark morning, in the rain and maybe fog, drivers just can't see a dark-clothed bicyclist. I see idiot, helmet-less, black-clothed ninjas pedaling at 5:15 AM, when I go in, and I think not only do they deserve to get hit, but then they should apologize to the driver.