The mechanics of panniers are simple. They come in pairs, and they have self closing hooks with which you attach them to the top rail of the rack. Pice of cake. They have a strap that serves as a handle and if you lift them by that strap, the hooks open and you can lift the bag from the bike's rack. A standard size for a pair of rear panniers is 40 liters. I think Ortlieb are the best. They are extremely rugged and from my expereince good for at least ten yeras of daily use. And they are waterproof, really. This particular model lacks some niceties, but in return it is rather cheaper - and lighter.
As for the rest of the gear, there are quite a few discussions here, but ultraliught means ultralight. So: two cycling pants, one pair of light trouers for in the evening, a few cycling jerseys, a sweater/fleece, and somethin glight against the rain. If you riude in spd shoes, you don't need other shoes. If you ride on racing shoes you obviously need light walking shoes as well. A Trangia 25 UL (for ultralight) is a nice meths stove for three. The alternative would be a gas canister stove, plus separate pans and a windscreen (same price altogether if you do not have light pots, and same weight).
Tents: good tents like Hilleberg are expensive. Do you have anything yet?
mattress: Thermarest Neoair is lightest and most compact and comfortable, but expensive. Closed cell foam is even lighter, cheap, but uncomfortable (good enough for the young).
Sleeping bag: PHD down bags are very light, good and expensive. What do you have?
In short try to make do with as much as possible with what you have, unless it is gigantic. Rear paniers and 15 kg each is possible without dramatic investment, and probably even less (there are three of you to share a few heavy items). Just don't take any unnecessary junk like chairs, extra shoes, extra clothing etc etc. The best luggage is the lugage you leave at home. Just google ultralight camping and you will get the idea.
You don't need to have punctures. I rarely do these days. You will need a good frame pump for high pressures: Zefal HPX is the classic choice. Finally borrow some accurate scales and use them mercilessly. You will discover that from the things you have like for example some shirts may be twice as heavy as other shirts. Use that knowledge.
Willem