In reply to ibexguiding:
On south-west limestone I started with a set of nuts and a set of hexes and about 8 short draws (I wasn't climbing anything harder than severe though). Once into HS/VS then cams 1,2,3 are helpful.
On grit or hard sandstone you will want a decent set of cams to start with really, as the cracks are often very parallel and grippy.
On 20m+ routes on limestone, granite, rhyolite, dolerite and similar I generally carry a set of nuts with doubles up to 7, full set of offsets, set of micros, cams 0, 0.5, 1, 1.5, 2, 2.5, 3, hexes 5,6,7, 2 short draws, 6 longer draws, 4 extenders. Over the shoulders I have 1 fat nylon 60cm sling with a screwgate (very reassuring if you get to lasso a tree), 2 120cm slings with screwgates (if you're on limestone then get skinny dyneema slings as they will be a lot easier to thread), 1 240cm sling with a screwgate. On the back of the harness I have nutkey, 3 screwgates, prussik, big boa, belay device. If the route looks like it'll take it then I also have a couple of bigger cams and hexes 8 & 9 (a full set of hexes is very useful for a lot of routes in the Wye).
If you can afford it, I'd go with double-axle cams (like the DMM Dragon) to start with, as you'll wish you did later down the line. They have a wider range and feel more secure in the rock.
I like to carry a lot though (more than most), as I don't like surprises. I don't ever want to leave the hexes at the bottom and then realise halfway up the climb that I need them, and I generally finish routes with a few draws left. I'd much rather that than use my last draw 10m from the top and have to improvise with other bits of kit or shit my pants and run it out. If it's a massive crack all the way up I'll probably leave the micros at the bottom though.....