I think you can get an 8x10 tarp very cheap. Even a low-dollar urethane coated tarp, which might be around a pound or so, will be a LOT lighter and easier to carry than any of those tents. And a LOT cheaper.
You can buy a budget 8x10 tarp for like $25-30 new. And a nice light Sil-nylon one for probably $75 new.
An 8x10 tarp with even the slightest learning about pitching, will keep you dry.
Poles and Stakes. If you are camping in the woods, you can use sticks for stakes. They work. You can use big thick sticks for poles. You don't need to carry poles unless you are going to camp on a parking lot or something. In the woods, you have sticks. Or you can tie-off your main ridge lines to trees instead.
Groundcloth. Go to your local hardware store and buy one of the clear plastic window film kits that are used to winterize windows and sliding doors. It's "polycryo" material, which is what many people around here use. Very cheap, light, and does the job. If you don't want to do that, you can buy a cheap mylar "space blanket" that is very light and cheap, and will work as a groundsheet, and is small and easy to carry.
Bug Net. You'll need one where you are going.
Go to one of the websites where they sell "Make your own gear"(MYOG) stuff, buy some no-see-um netting, and order enough to make a suitable bug net tube that can go around you when you are in your sleeping bag. Or even a little more if you want to make a little bug-net inner tent for under your tarp. You can sew this together very easily, even if you have to hand-stitch it, and you'll have bug protection.
It also works as a protection from condensation dripping down off the tarp in certain weather conditions. And you WILL be having some of that too.
So, make a bug net system for yourself.
Sleeping bag. Get one you can afford and is as light as you can find for the temperatures you will see. Bear in mind that many of the low-priced sleeping bags are unrealistically rated, and will NOT really keep you warm at the temps they say they will. But if you ask around here about some bags, people will help to steer you the right way to get a bag you won't freeze inside, and won't blow the budget too bad, and you can carry it without a wheel-barrow. I agree with the others on this thread who say to get a good quality bag.
Sleeping pad. You need a pad for more than just comfort. If you are sleeping in cold weather it makes up half of your insulation, and protects you from the ground cold. It's important. You can get by with an average inflatable pad in the cold weather by using a closed-cell foam mat under it, or over it. These ccf mats are cheap, and are good ways to add insulation factor to your pad, and if your inflatable pad goes flat, you have at least some form of back-up, even if minimal. For the money, I would take a look at a Klymit Static-V, or a used Neo-Air if you can find one fairly cheap. People are buying the latest Neo-Air models now, and you might find a used one from last year for a price you can afford. If you don't mind sleeping on a harder surface, you can get a Therm-a-Rest RidgeRest for quite cheap, and they are good starter pads for somebody young who can handle harder sleeping surfaces. If you combine the inflatable and the ccf pads, you have a winter system.
Pack. AFTER you get your other stuff, THEN find a pack that will fit what you need to carry. If you buy the pack beforehand, it is highly likely that it won't be the right size for the gear you end up with. You can find used packs here on the Gear Swap page which will do you just fine, and any "hand-me-down" pack from the UL backpackers on this site will be good for you, as long as it is the size that you need.
Then you just need some clothes and shoes that are appropriate.
This stuff doesn't have to be ultra-expensive to do. You can refine your set-up as you go along. Most people do that.