In reply to Shane jones:
Almost assuredly you'll be best off with half ropes, also, confusingly, known as double ropes. These are generally supplied with diameters from 8.0mm to 9.0mm. I tend to go for the thinner end of this range as I'm old and like to minimise weight on the approaches (but beware - thinner doesn't always mean lighter - check the weight per metre when researching). The Mammut Galaxy 8.5mm and Beal Cobra 8.6mm are very widely used and well thought of for handling as well as durability. There are many others.
Ask yourself if you need the top rated "superdry" ropes. These are particularly beneficial for British Winter, Waterfall ice and Alpine climbing, but the process they undergo in manufacture makes them better in all uses as the internal fibres move more readily against one another. That said the 50 metre half rope I have for use in the UK is not dry treated.
Another thing to consider is the length you need. Many just go for 60 metres as it's suitable for anything you might find in UK and abroad. I find that on most UK climbs, particularly on outcrops, but also in Wales and The Lakes for instance, they tend to be rather longer than necessary as pitches are often short. I go for 50 metres in UK but also have the luxury of a 60m for foreign use.
being from the North I tend to favour Northern retailers and I'm sure there are equally well thought of elsewhere but have a look at Needlesports of Keswick and Rock & Run. Both have a good range to offer.
My usual partners and myself never buy pairs - we assume the guy we'll be climbing with will bring his and thus save the expense.