14 miles each way here. 5 days a week unless I'm offsite for some reason. Been doing that for ooh, about 15 years now at different workplaces.
I have a suit in work just in case but rarely use it.
Mostly I just take a shirt in each day and trousers at the start of the week. Fridays is dress down day so jeans and t-shirt then.
Shoes in work.
I take spare shorts and riding shirt in every day. Partly becuase putting on sweaty clothes is pretty nasty but also, if it rains, you'll hate it. Putting on cold, wet clothes at the end of the day will put you off for good.
I have some shoe driers under my desk for at least drying my shoes out a bit but only after they've had a few hours with newspaper inside them.
i always keep some danger pants and socks in work. Saved me a few times they have.
You can fold a shirt up neatly and it'll be fine when you get to work. if not, hang it up next to the shower for a few minutes. The steam irons it.
Use mudguards if you want but if it's really wet they'll make no difference. Don't bother with waterproof clothes, you'll sweat more than the rain will wet you. Don;t bother with a waterproof bag, put everything in carrier bags.
What else? Expect a load of ridiculous questions about which charity you're doing it for, how did you lose your license, can't you afford a car?
Take tools and spares each way.
Work out a nice route. It may not be the most direct route but a scary, traffic-logged route will demoralise you. my direct route is about 10 miles but right now I'm doing the 13 miler in because I'm on a road bike. Once my crosser is working again I'll be back to the 50/50 on/offroad route that I love, very little traffic.