There are a few elements to look for when choosing a coffee grinder.
Grind Quality: You buy a bag of awesome whole coffee beans from your favourite roaster and now you need to crush them. This is where your choice of coffee grinder will determine an ok cup of coffee or a great cup of coffee.
The first thing to look for is the burrs. This is the cutting mechanism that will grind your beans ready to brew. You want to avoid coffee grinders with blades. It's basically a blender in disguise. It will cut your coffee it tiny shards rather crush your coffee into a powder-like form.
So look for burr grinders.
Ease of Use:The easier and simpler something is the more you are likely to do it. So you want a grinder that suits your time and skill level.
There are grinders that will weigh everything for you and grind. Or you may like the idea of using muscle power and no wires or cables.
Price: Good electric coffee grinders aren't cheap. Maybe a hand grinder is a place to start. There are somevery good hand grinders under £50.