My folks went on an extended outdoor hikes and camping for days 2-6 of their honeymoon, although thankfully sanity returned with age and children. However, I've done this many ways and many times, and based on your descriptions, would recommend the following as a minimum starter kit:
1.) Tent -- some sort of decent Coleman tent with an integral rain topper, which form-fits over the tent and ties to the same stakes as the tent itself. Unless you expect to be camping in massive downpours, this will keep the bulk of the moisture off.
2.) Small plastic tarp -- not for keeping things off the top of the tent, but rather off the bottom. Something roughly 8' x 8', folded into a quad, is a far better thing to set your tent on than the bare earth in many places. Also, it's easier to wash and dry a tarp later than it is to wash and dry a nylon tent.
3.) Roll-out foam mat -- If you don't take one of these the first time, I guarantee you will the second time.
4.) Sleeping bag -- this doesn't need to be an elaborately expensive affair, but I do recommend some sort of nylon shell with a better-than-basic nylon insulating fill. These are both warm and light, which will prove a great asset later if you ever have to carry it for a while.
5.) Water canteen or equivalent -- a Nalgene bottle or small insulated water jug also works.
6.) Yesterday's newspaper. Not only is this great for starting fires, a wad of paper in your shoes will dry them out overnight after yesterday's accidental forray into the creek.
7.) Miscellany -- Two small LED flashlights (one to use, and one to have handy when the first one doesn't turn on at 3am when you wake up suddenly and realize you really
need to relieve yourself). A swiss army knife or leatherman utility tool. A butane lighter and a book of safety matches as a backup. A small first-aid kit (basic bandages and disinfectant, plus Rollaids and aspirin or equivalent, and calamine lotion if you have poison ivy/oak in the area). Small can of insect repellant. A few packages of tissues for nose or emergency restroom duty. Small packages of alcohol-based hand wipes (good for general sanitation, removing pine sap, or sterilizing that knife if you get a splinter). Travel-size kit of your standard personal hygiene products. Granola bars for random snacking. A small backpack or travel bag to hold all of these at arm's reach. A suitably-sized, water-tight plastic container to hold the water-sensitive items.
If you can get your hands on that much, you can do basic overnight in a tent without resorting to lopsided barter or outright unpleasant, uncivilized things if something unexpected comes up. It's a whole different ballgame if you get into backcountry, extreme weather, or food preperation, but...baby steps