For a wet commute.
In the summer - the same as what I wear for a dry commute. Lycra s/s shirt, shorts and baggies. Getting rained on in the warmer months is no problem. Lycra dries very quickly.
In the winter. Sealskins Waterproof socks ( They work for some people, not for others), under the baggies I wear leggings. On top, long sleeve jersey and a waterproof jacket. For very cold temps I wear a
Altura Nightvision Evo. For milder winter temps, a Montane Featherlite.
For shoe coverings, over the years I have found there is no point. Water will always get in due to the holes in the bottom for cleats etc. Waterproof trousers, once again there's no point imo, you just get that boil in the bag syndrome.
Preparing the bike. My commuter get's cleaned and re-oiled/lubed every week regardless of weather, and once a month a full strip down, deep clean, re-lube/oiled and greased. I do a 30+ mile round commute so need the bike working properly always. Cleaning it is a good way to spot any potential problems of which I fix rather then leaving it another day and regretting it.
I check my tyres before or after every ride. Dig out anything that is stuck to the tyre, otherwise anything stuck in the tyre will work it's way in and cause a puncture. So try to get into the habit. This year, touch wood, I haven't had any punctures on my commute.
Bonus point.
I carry everything in panniers. I used to use a rucksack, but found it far too uncomfortable and cumbersome.