It’s worth spending money on a decent lock, as lock strength can vary enormously and you generally get what you pay for. It’s advisable to spend at least 10% of the cost of the bike on a lock – and using two different types of lock will help to deter thieves. See the LCC info on Bicycle Security for more information on types of lock.
You don’t need to overload yourself with accessories when you first take your new bike out, but a pump and a spare inner tube or puncture repair kit is sensible. You’ll also need a small spanner or allen key for removing the wheels (unless they are quick release) and a set of tyre levels (ideally plastic) for removing the tyre. Most pumps fit both Presta and Schrader valves these days, but do double-check with your bike shop if you’re not sure which you need.
Unless you’re never going to ride your bicycle in the dark or poor visibility, you will need a white front light and a red rear light. You can use flashing or steady lights: a steady light is recommended at the front when the cycle is used in areas without good street lighting. LEDs are the most popular type of light; they usually run on AA batteries. These will need changing regularly. Rechargeable systems (usually halogen) are very bright, but also require a lot of power and need recharging frequently. Dynamo generators are the cheapest systems to run as they do not require batteries (they are powered by the motion of the wheel), but a little more complex to install.
A note on helmets:
LCC takes a neutral stance on helmets. If you choose to wear a helmet it’s important to remember that helmets do not, unfortunately, prevent cars and lorries from hitting cyclists and so can never be a complete safety measure. If you buy a helmet, make sure it’s the right
size, properly fitted, and comfortable. A poorly fitted helmet will not only be less effective, it can actually make injuries worse in certain conditions. Your bike shop will be able to advise you on helmet fit.