Bike computers have improved a lot since the early days of cable operated analogue speedometers. No longer do we have a gauge in a housing the size of a city clamped on the bars by a dodgy jubilee clip.
A good basic bike computer can tell you how fast you're going, how far you've gone, and how long you've been riding. More advanced units can tell you all kinds of useful information, such as your cadence (revolutions per minute of the cranks), trip distances, pre-planned trip distances, your heart rate, lap time, max speed, average speed, temperature and pacer functions (which lets you know if you're going faster or slower than your current average speed).
It's all well and good having loads of functions, but they must be presented in a way that's easy to read when you're out riding your bike. The controls must be easy to use, even when you're wearing gloves, and the mounting for the head unit must be versatile enough to fit standard and oversize bars - likewise the mounting for the sensor/s for speed and cadence. It shouldn't be too much of a pain to fit, and it should also be easy and quick to set up for your bike.
Ideally, the instruction manual should be clear and lead you through fitting the computer in a simple step by step manner, and gradually take you more and more in depth once the initial 'get it out the box and play with it' period is over.
Wired vs Wireless
If running wires from the head unit at the bars to the sensors isn't an issue for you, then wired is just fine. If getting results without the risk of interference is what you want, then wired it has to be. But... if the thought of running wires along your bike is a little daunting, then choose wireless. A wireless set-up will allow you to swap a computer between bikes more quickly and easily than a wired system, and your bike will look a little prettier without the wires, if that's important to you. Wireless systems can suffer from interference, and the transmitter requires a battery or batteries as well as the head unit (and sometimes separate batteries for the head unit mounting too). More expensive systems tend to be wireless by default, seeing it as an added feature, but in truth some of the more advanced systems could benefit from being wired to increase reliability and reduce the risk of crosstalk or interference from other sources of electromagnetic fields.
A large clear display that is easy to read and shows more than one bit of information at once is essential.
They need to be positive in their action and usable with gloved hands when cold and wet.
Head unit mountings
Should be easy to fit and adaptable to suit all kinds of bar sizes and shapes.
A wired system has a wire running from the head unit, or the head unit mount, to each sensor.
There are no wires running from the head unit or the head unit mounting to the sensor or sensors.
Should be easy to fit and be able to cope with different sizes and shapes of frame and/or fork profiles.
Attached to a spoke, triggering the sensor as it passes on every turn of the wheel. Beware: some magnets will not fit flat-bladed spokes.
A sensor mounted on the fork or frame is triggered by a magnet mounted to the front or rear wheel spokes to measure revolutions per minute. Because the head unit knows the rolling circumference of your wheel, it can calculate speed. Because it knows speed, and it has an internal clock, it can calculate distance travelled, average speed, and so on.
A sensor lives on either the chainstay or the down tube, and a magnet on the back of the crank arm triggers the sensor to measure the revolutions per minute.