I climbed without my own rack for years as I partnered up with people more experienced and used their rack. A 50m rope is a good start although you can get away with a smaller one 30/40m if you only want to climb on short crags like most of the Peak. 

Depending on what you can afford go for the lightest gear ( a full rack is a hefty weight to haul up a climb!) but most well known makes will be fine. Some people have 2 sets of nuts and use different manufacturers, can't say I've ever developed a preference for any particular make.  

quickdraws - 8

slings  - a 240cm, 2x 120cm 3 x 60cm

hexes - 3 or 4

1 set of nuts (you'll need a 2nd set later)

This will get you up lots of easy climbs and you'll be able to add cams (1- 4), more nuts and all manner of extra shiny goodies at a later date 

try http://www.andy-kirkpatrick.com/site/articles for good articles about selecting gear, ukclimbing.com for gear advice and items for sale (try searching for 'first rack' on the forums)

Climb magazine on line has lots of old gear advice columns - http://www.climbmagazine.com/gear-articles.aspx?id=6b09c7ec-c97d-4ade-9f91-1e1831a94358 (you'll have to register first

I agree - do a course, join a club - it's a great day/weekend out. Apart from anything else, realistically you're several hundred pounds down before you can lead a single climb, whereas in a club you can share/borrow gear to get started.

There's a great list of things to buy at Needle Sports that I found really useful, and they're pretty cheap, although V12 and Joe Brown in Llanberis are the cheapest I think (all 3 do free delivery).

Enjoy it - hopefully we'll get a dry summer this year at last.

without meaning to sound rude dude, but, if you need to ask this question then you really are not experienced enough to be leading just at the moment.

there is nothing wrong with going on a course to learn the techniques, join a club to gain the time/ experience and slowly build your leading experience and kit up. A club is a good way to try other climbers kit and saves having to dish out for expensive kit mistakes. there is loads of fancy kit out there, but not al that glitters is gold.

safety first- it makes the fun last longer.

Rack, depends whats at your local area in regards to being able to place protection.

Differences between manufacturers becomes personal pref, I have Wild Country hard ware, but a whole mix of other brands too, just because I got a good bulk deal at the time.

A set of 1-10 on wires, some bigger ones on tape if appropriate, lots of slings, quickdraws,  I have a few cams and another set of wires too, but build up gear over time.

Rope, good quality 50m will see you good for setting up anchors etc.  10-11 mil single rope is a good starter.