A temptation is to try and make a bike too versatile when the far easier solution is two bikes. I did this by accident having started out with the wrong sort of bike for my commuting needs. Then I built up a dedicated commuter to include:-
big tyre clearances, puncture resistant tyres, full mudguards, rack, variable hand position handlebar setup, relaxed geometry, hub gears - I love hub gears for being able to change whether moving or not and you don't chew through chains and stuff.
The changes I've since made to that concept:-
disc brakes, dynamo hub and lights and am looking to change to vertical dropouts with either a chain tensioner or EBB - all about making the inevitable punctures as easy to sort as possible.
My original plan was that this heavy beast would be a Winter and wet weather commuter, taking the lightweight bike on nice days. As it panned out I found that there was enough contrast between lousy and good weather riding to make it feel like a different bike, and I was fast enough on it. Plus it made the weekend bike feel far lighter, and more special, when I rode it. Everyone will have a different take on this but I found I was happy just to stick with the heavier bike all the time on the commute. But the commute was very free flowing, with only 2 sets of lights over the whole 20 miles. The bike was more of a mile muncher than a nippy beast for weaving amongst traffic.
I ride flat pedals so don't have limitations on my footwear, but I wear grippy MTB shoes to commute in, I do have some overshoes but wear them very rarely, it has to be really wet or very cold. To be honest rain was a far bigger concern before I began commuting than it turned out to be in reality. I'm running at about 4 proper soakings per year, but with full guards etc it does have to be very heavy rain to soak me. A locker at work is fantastic, I kept my suit, ties, shoes, toiletries etc when I still had the very long commute. I kept two pairs of trousers and one jacket and one pair of trousers went to the dry cleaners near the office each week. Each day I took in a towel, underwear, shirt, lunch and fresh cycling kit for the way home, that all fitted easily into one pannier(Ortlieb Backroller Classic). I could also fit my laptop in as well but preferred not to if it could be avoided. By having fresh kit for each way I wasn't concerned about getting wet in the morning or getting kit dry through the day. The shoes I just left out in the changing room to dry off, once or twice I cycled home in wet shoes but you don't notice after a couple of miles.
As I say worries about weather and how heavy/quick the bike is didn't seem to matter once I got going.