On my non-catering tours, 2 panniers are enough. I also carry a bar bag on a quick release mount for carrying valuables and holding a map.
If your sleeping kit wont fit inside your pannier bag you can strap it on top of the rear rack. You can use plastic bags or nylon drybags for protection.
I used a very cheap and small solo tent, a 3/4 length thermarest style mat. For commercial campsites you need some privacy but for wilder/primitive campsites, a simple nylon tarp may do the job. I suggest you keep everything simple, cheap and lightweight to start with.
You can find packing lists around the net but don't overpack.
Don't take tools that you cant use. As long as your bike is in good condition to start with it should be OK. On a week's tour, a chain tool and spare powerlink is really the only special bike bit you need.

You can take quick drying clothes and wash them at night. 3 of everything is about as much as you need, 2 in good drying weather.
Minimise your footwear.
For non-cooking, I took a spork (or plastic disposable utnesils) and swiss army knife. If I need a cup, a coffee machine disposable one will last a week. Some people take brew-kits eg solid fuel sterno or alcohol gel burner and a metal cup.

Read up on some ultralight camping styles.