On a nice sunny day there's no reason why you shouldn't slop about town in your shorts and flip-flops - no special clothing needed at all! But once it starts getting to be winter, you get to a point where a few bits of well thought out fabric will keep you warm and dry. There's no need to rush out and buy everything at once though - add layers here and there as the nights draw in.
Cycling can still be comfortable, even if it's cold wet and dark out there. While ordinary clothing is often fine, cycling-specific clothing makes your life easier and more pleasant for a number of reasons. The cut is more comfortable, as it takes into account the riding position. Cycling tops require lower backs, because you are leaning forward, and sleeves need to be extra long because your arms are stretched out. Shorts and leggings need to come up high, to keep your kidneys warm. Legs need to be stretchy or baggy, so your knees can move.
Windproof material keeps you warm. Wind chills you, especially if you are wet. As you cycle, you create your own wind. Waterproof clothing keeps you dry from the outside. Breathable clothing keeps you dry from the inside. Showerproof clothing will not keep you as dry for as long as waterproof clothing. Some fabrics (especially synthetics) dry relatively quickly. This is useful, as you may have to put the same clothes on to cycle home after work.
Normal clothes can suffer badly when used regularly for cycling, especially shoes. It's more economical to buy cycling-specific clothing, and not destroy your normal clothes, if you cycle a lot. Bright colours can make you more visible, although not necessarily more attractive.
A Fabric Glossary:
Gore-Tex: this fabric is waterproof, breathable and windproof. It is good value for money, although relatively expensive. Clothes made of Gore-Tex are very warm, as the heat created by your body when cycling cannot easily escape. So you don't usually need as many clothes underneath (too many bulky layers also affect breathability). Gore-Tex can be washed in your machine using Grangers' fabric wash. The outer layer of waterproofing can be reactivated by tumble drying the garment at a warm setting.
Lycra: life on earth without lycra is impossible to imagine. Different weights are available, thicker lycra is more comfortable, more durable, blocks more wind, and is more expensive. Cycling shorts, leggings and bib tights are usually lycra based. More expensive shorts and leggings are usually made with wicking fabrics increasing their comfort.
Whatever you choose, make sure it fits you well. Try sitting on your bike before you decide whether a garment suits you. Make sure the sleeves don't ride up and expose your wrists when you reach forward for the bars. The bottom of a jacket should cover your bottom, but not catch on the back of the saddle when you put you foot down. Check yourself in the mirror, too – you have to wear this stuff!
Choose layers that can be used in various ways – for example, a summer cycling jersey is a good investment, as it can also be used as an extra insulating layer in winter.