I would go for a small 3 person tent which would give you enough room for 2 plus space for kit and admin if the weather is not what you want to be out in. Something like this:
http://www.vaude.com/epages/Vaude-d...ps/Vaude/Products/15805/SubProducts/158054000 - tarps and hammocks are nice, I love 'em but the reality is that i'm going to be sleeping in it so the view isn't that important with my eyes closed.
2 insulating mats to sleep on (my preference is thermarest but exped down ones are supposed to be good and alpkit are ok too)
I would opt for a double sleeping bag - the only seriously warm ones are crazy prices but fortunately, it turns out that sleeping bags are like gloves... fingers in gloves are colder than mittens... two people in one bag adds at least one full season from my experience.
As mentioned, something to stuff jackets or a jumper in to be a pillow.
For cooking, I like simple... one pot... you can still be creative and cook nice things but it just requires more thought. If you're allowed fires make sure your pot can handle it, so no plastic bits sticking out. Stoves - no real preference, if you're going for one that attaches to the gas cannister directly, invest a few quid in a little tripod legs thingy that clips to the bottom of the gas for stability.
Head torches... get one each, if you're bribing your wife along, include her properly... get a shewee if you're wild camping and get her a knife, a mora costs £10 and isn't a big loss if she decides she doesn't like bushcraft.
For foods starting out, I like wayfayrer as they are so easy and taste pretty good (the chocolate puding is the daddy) - if you're getting up to speed with all the other aspects as a couple, last thing you need is dodgy food... just boil the bag and use the water for coffee/tea and what's left for washing up.
Dry wash for cleaning your hands and wet wipes are perfect for a weekend away for wiping your face, pits and dangly bits. Things like foot powder are good if you're moving a lot. Basic first aid kit should always be with you while camping, if you're cooking, pack first aid for burns, woodcraft projects, pack something for cuts and drinking, pack resolve