Wiggys and woods bags are fine, but like I said, warm, light, cheap...pick two. I have a woods and a wiggys and they are far from backpack friendly. I am unaware of the gi down bags mentioned, but if they are indeed warm, light, and cheap you may have found the unicorn. I think light might be a relative term to some. I go mad when I try and do any backpack trips with a total pack weight before food of over 15 lbs. A sleeping bag like mine is a huge part of that and of all things a bag should not be skimped on at all. Mine is a shade under two lbs and is good to an honest -7 celsius. Pack and sleeping pad are the next big items and depending on the trip use either a gossamer gear gorilla at again, just under 2 lbs, or a Badlands sacrifice if I need to carry a bit more weight. It is about 3.5 lbs. Took it to Cambodia and it was awesome. For a sleeping pad, a prolite, or prolite plus a ridgerest if things will be colder. My tarp is an 8x10 and weighs about a pound, and summer fill enclosure bug net is like six ounces.
That gets a pack, sleeping bag, and pad to about 9 lbs. My stove kit is a wood burner, so it is about a pound for stove, and pot...that's 10 lbs for the big components. The rest is an extra down or fleece jacket of whatever type, packable raingear, extra socks, random bits, headlamp, toilet kit and you are at about 13.5 lbs. homemade freezer bag meals are incredibly light, so figure on about 2.5 lbs of food a day. My kit has been exhaustively tested..and these numbers are with a pack that can haul seventy lbs if need be ..
My winter hot tent kit is obviously heavier, but includes a titanium woodstove and hot tent.
I know you are trying to keep things cheap, but I feel like gear you are relying on to sustain your life with when miles from home on foot needs to be a more personal thing. Each person needs to find a system that works for them Imo, a light pack greatly adds to the enjoyment of any hiking trip, and adds a degree of safety as well. heavy packs equaln sprains, strains twisted ankles and fatigue. I can and have outfitted people for next to nothing with gear. Nine dollar foam pads work fine from an r value perspective, cheapo packs can be found (even made a few that were cheap and worked great) cheap tarps can be had that are almost as light as silnylon for under ten bucks, or even a passable tyvec shelter can be made for free. Alcohol or woodgassifying stoves can made for.free. I have several homemade ones and they work great. Cheap headlamps work well, and you can sleep with a bug jacket over your torso, tied up to your tarp ridge line (I have done this, works fine) i can literally put together a kit of all you need for about 150.00..
But I will never ever suggest an inexpensive sleeping bag! That is where you should spend the better part of your budget Imo.
And that sir, is just my opinion!