In reply to finn rc:
60 meter for a single rope is pretty standard and for good reason (the convention is sport pitches are very very rarely longer than 30 meters so 60 gets you up and down safely) I wouldn't bother with a 70 or 80 meter as you just pay more and 99.9% of the time you will just have to coil more spare rope. Really the only benefit of long ropes is running pitches together but you tend only to do that more with experience climbing outdoors which you wont have yet (and also heavier for long walk ins!). And shorter ropes would be good for grit stone cragging and outcrops but you dont really save that much money if you buy a 50 meter and will always have to be careful about not lowering off the end of your rope. (Happened to dave mcleod so happens to the best of us!)
Diameter is roughly 10mm. Most ropes are 9.8mm. The trade off you are making is between handling vs durability. Slightly skinner ropes say like 9.1 pay out quickly through a belay plate and feel 'supple' and easier to handle and are lighter for max effort pitches. The down side is they dont age as well and probably will show signs of wear quicker. So a nice beafy 10.5mm rope is much more resistant to getting rubbed over rough rock... the downside is they pretty quickly turn into fat and stiff ole pigs. So they have to be forced into belay plates and just generally handle poorly and weigh more. So 9.8mm is the compromise most people settle on. You can choose whatever diameter you want, go fatter if you're going to be doing lots of top roping on abrasive mountain rock and you are lazy with rope protectors, and go skinner for limestone trad.
Various 'dry treatments' add quite a bit about 20-30% of a cost of the rope. They stop water getting into the core of rope and then freezing stiff in winter climbing (unlikely to be doing on your first rope) but they also stop grime getting in too. Allegedly make ropes last longer. Ive always had dry treated ropes and had good service from them and I like the mental reassurance. Always good practice to use a rope bag and keep your rope out of the crap and sea.
tldr: 60 meter 9.8mm rope from any major brand (edelweiss, petzl, dmm, beal, tendon) and dry treatment if you have any money left.
https://www.bananafingers.co.uk/single-ropes/edelrid/heron-eco-dry-98mm - this sort of ting. £140 so bang in the middle of budget, dry treated and will do you well)