You wouldn't change into special clothes to get the bus or get into the car would you? For typical, short distance commutes, it's perfectly OK to wear your normal clothes. The key to this is your bike: mudguards, chainguards and standard pedals allow you to wear regular clothes and shoes.
If you like to ride fast or your commute is at the longer end of the spectrum, you'll be more comfortable with some sort of performance oriented clothing. However, you can do this and look fairly normal. A good quality synthetic or merino wool base layer can effectively convert any top into a cycling top.
Similarly a pair of padded under-shorts, teamed with a pair of lightweight shorts or trousers, are comfortable for long rides, yet will allow you to blend in anywhere.
There are ways to stay visible, day or night, without resorting to the dreaded day-glo. By day, bright red is a highly visible colour that doesn't clash with everything in sight. By night there are plenty of subtly styled cycling jackets with reflective Scotchlite panels that come alive at night yet are invisible by day.
Many perfectly fashionable, aesthetically minded folk seem to lose their sensibilities as soon as they climb aboard a bike. When buying your accessories, jacket and helmet, make an effort to either match or contrast your colours. Don't forget to take the colour of your bike into account too. The whole lot should form a seamless, matching ensemble. Easy peasy.
Good helmet fit is of course the most important thing but certain helmet styles suit certain head/face shapes better than others. When buying a helmet, try on as many as you can until you find one that looks good and fits well and conforms to the relevant safety standard.