Clothes: layers are good (as your can add or remove clothes as appropriate). Avoid jeans (unpleasant when wet!) and very loose clothes (e.g. floaty skirts).
Winter: wind-proof gloves make a big difference, breathable waterproof jackets, trousers and overshoes also help.
Go for shoes with firm soles, or special cycling shoes (it's also good to invest in toe clips which stop your feet from slipping off the pedals and increase your pedalling efficiency).
Buying a helmet
There are three types of helmet: hard-shell (usually moulded from plastic), micro-shell (with a thin outer layer of plastic), and no-shell (light with a soft surface).
Your helmet should be marked CE (it shows it has been approved by the EC), some helmets also have a BS Kitemark (BS6863) or the ANSI (ANSI Z 90.4) AS (AS 2063) or SNELL Foundation stickers. These show that they are made consistently of a high quality.
Buy the smallest size that gives a snug fit. When you have strapped on your helmet, it should not move backwards and forwards or from side to side. Check that it is comfortable and doesn't restrict your hearing and vision. Look for a helmet with ventilation slots to keep your head cool.
If you squash, scratch or knock your helmet replace as soon as it is damaged. All helmets should be replaced after a few years, even if they have been carefully used.
Avoiding punctures
Go for good tyres (some have anti-puncture reinforcement).
Your bike shop can fit anti-puncture tape between the tyre and inner tube.
Opt for good quality inner tubes.
Your bike shop can provide anti-puncture sealant which is squirted into the inner tube through the valve. This seals any small holes from inside.
Keep your tyres well pumped up (so that less tread surface touches the road).
Take a spare inner tube and puncture repair kit with you.
At the end of your ride, check your tyres for glass, thorns, stones, etc. and remove them so that they don't cause problems on your next ride.
Safety
Wear light, bright, (fluorescent if possible) colours during the day. At night, add reflective materials. These are best applied to your rear (e.g. on the back of your jacket, sashes, arm and leg bands, and on the backs of your shoes). Every bit helps!
You should add reflectors to your pedals, and at the rear of your bike. You can also add reflectors to spokes, mudguards and cycle bags.
The Road Vehicle Lighting Regulations demand that bikes used on the road between sunset and sunrise must have lights and reflectors. The minimum requirement is that you have a white light at the front, a red light to the rear, a red rear reflector and amber pedal reflectors. The lights must conform to (and be marked with) British Standard BS6102/3, and the reflectors must be market BS6102/2. You can also mount additional lights and reflectors on your bike (and these do not have to conform to the British Standard).
The Government are currently considering changing the law to allow flashing lights on cycles (as long as the BS standard steady lights are also fitted). It is proposed that the flashing lights must match the colour of the steady lights e.g. white at the front, red at the rear.
Riding about
Know your highway code. It applies to cyclists too!
Be considerate to other users, and give way to pedestrians and horse-riders on traffic-free paths and bridleways.
Take particular care at junctions, when cycling downhill and on loose surfaces.
Ride in single file on narrow or busy roads.
Consider wearing a helmet and high visibility clothing.
Fit a bell and use it - don't surprise people.
Take your place on the road confidently; clinging to the gutter will only increase the risks, as other traffic may not see you, or try to squeeze past you. Try to ride at least a metre from the kerb.
Signal clearly and take up the correct position in the road in plenty of time. Try to get in front of the traffic or into the middle of the lane at lights.
Avoid swerving to avoid a pothole. Lift yourself off the saddle as you ride over it where possible
Security
Mark and register your bike with a registration company, or with the Police. Make sure that they mark your bicycle in two separate clearly visible places, with a tamper proof label.
Always lock your cycle when leaving it, even if it's only for a few minutes. Lock your cycle through the frame, secure or remove the wheels and remove smaller parts and accessories (e.g. lights, pumps).
There are three main types of lock: coil/cable locks (these use plastic-coated steel wire, they're cheap, light and easy to use, but are easily cut and best for short-term parking in low-risk locations), chain and padlock systems (the heavier and more expensive the more secure), shackle locks, which are also called "U" or "D" locks. These are regarded as the most secure (the more expensive, generally, the better security and quality).
Get your bike insured, either by extending your household insurance, or by taking out a separate policy.