Any good helmet is going to fit snugly, so it's gonna flatten your hair. I don't think there's a way around that one.
If your bike doesn't have racks or baskets, a backpack is probably the simplest solution. But panniers are probably the better option, as you don't get as sweaty, and the lower center of gravity makes your bike more stable.
In terms of not getting dirty, probably the best option is to go lycra (there's a reason serious cyclists wear it) and get changed at work. You can get clips/bands to put around your ankles to keep your pants from getting caught, but on a wet day you are still going to get splash from the road.
Also, when you oil your chain, make sure you wipe off the excess. Not only does this ensure your chain and gears last longer (excess oil turns into a gritty abrasive paste), but it won't splatter over you.
Carry a pump and spare tube, and know how to change a tire. If you ride long enough, punctures are inevitable. Replace the tube with the spare, then fix the puncture at home.
The reasonable man adapts himself to the world; the unreasonable one persists in trying to adapt the world to himself. Therefore all progress depends on the unreasonable man.
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