Actually, polystyrene cycle helmets are probably of no use whatsoever in any serious accident, and might even lead to an increased risk of neck injury. Don’t fall for the propaganda - see http://www.cyclehelmets.org/
I do sometimes wear a helmet, but mostly when I’m riding off-road, to protect from tree branches etc. If you get hit by a car a helmet is very unlikely to do anything. BUT cycling is statistically ~30% safer than walking on a per-mile basis.
Kudos for considering cycling – I got rid of my car at the start of the year and have been commuting to work by bike - train - bike instead of car - train - Tube. It has cut about 20 minutes off the total journey time, and 35% of the cost, and I now cycle 15 miles a day so I feel a hell of a lot better.
I change my clothes completely upon arrival: on the trip in, underthings can get sweaty and overthings can get wet/dirty/wrinkly. So I keep a couple changes of clothes at work and always carry a stash of clean socks and undies. Changing into something clean and dry after arriving has greatly enhanced my quality of life.
I don’t carry a lot of tools because I pass no fewer than eight bike shops on my way to work. But I still don’t leave home without my tire pump.
Depending on your workplace circumstances, this story may be useful: at my former job, the Bike User Group worked and lobbied and so on and so forth until the employer installed a shower for their use. The employer was finally convinced that it was consistent with all their corporate mumbo-jumbo speak around (a) employee health and wellness, and (b) lower-impact commuting.
(Bike User Groups are also a good way to pool tools (once I needed a chain breaker to get home; the BUG was very useful) and tips. I’ve had them at a number of workplaces and they’re great.)
My current employer has a shower and wins a Clean Air Commute award every year.