The first thing to consider is your budget. You will hear many people say that you should go for the most expensive that you can afford. But you need to take into account that a big brand name mattress, in a big chain store, for lets say £200, wouldn't be as good as one made by a smaller independent manufacturer, and bought from an independent on line retailer, for £100.
So if you want good quality at a low price, then stay well away from any of the big brands, and big retailers. And instead buy one made by a smaller independent manufacturer, from an on line retailer. But most importantly make sure that they give a proper 100% satisfaction guarantee, that allows you to unpack and sleep on the mattress (many retailers won't allow this with mattresses).
You will see many people saying that you should go to a bed shop and try mattresses out. The problem with this is that it can give you a false sense of security. This is because laying on a bed for 10 minutes in a shop, fully clothed, is only going to give you a very rough idea. And it isn't going to tell you what it is like to sleep on. Remember most (not all) retailers won't take mattresses back if you don't like them.
If you are on a low budget, then you may be better off with a decent quality open coil sprung mattress. You can get a decent quality, 8" deep one for around £135. Or if you want to go up to a 10" deep, high quality one for around £150.
If you can afford a pocket sprung mattress (that will give far better support), then stay between 1000 and 1800 pocket springs. And you can get a good quality 10" deep one for under £270.
Someone said that you should use a box spring (known as a sprung divan base in the UK). Well this is complete rubbish, and is a tactic used by sales staff to get you to spend more.
If you have a slatted bedstead, then open coil sprung mattresses will be absolutely fine on it. With a pocket sprung mattress you would need to lay a sheet of thin hardboard over the slats to stop the springs trying to push through, and becoming damaged.
If you have a divan base, then this will be suitable for any type of mattress. JUst make sure that there are no dips or soft spots on it, and that it is still level.
Ignore the mattress brands site that someone mentioned. It is just a click through, advertising site.
Avoid non turn mattresses, as they won't last as long if they can't be turned.
Pillow Top mattresses that look like they have a quilt sewn onto the top of them, are one of the worst gimmicks on the market. So avoid.
Foam only mattresses can be very hot and sweaty. And the foam can start to break down over time, leaving a dip.
Don't use inflatable mattresses for long term use.
Contact the seller, telling them your budget, what type of base it is going on, how firm you like your mattress, your previous mattress (and if you liked it or not), and your rough size (if you are very small or large). And they should be able to give you the best advice. If it sounds like they are just trying to get you to spend more, then go elswhere. If they give a proper satisfaction guarantee, then it is in their interest to make sure that you make the right choice the first time, otherwise it will cost them money to exchange it.