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!

North Face Blue Kazoo - a goose down mummy rated for 15 degrees. What Hutchy said is exactly right but I will also add that nothing compresses like high quality goose down. That means there is an extra benefit to spending the money for warm and light and that is it will be the smallest package possible in your pack.

So about how big are they compressed and how much do they weigh?
The Western mountaineering ultralight?
The Mummy GI?
The Wiggys?
The North Face blue kazoo?

Hutchy- What size is your pack? How much is the total weight? I was thinking about going with a 70L. I hoping to make it with each person (5 people total) carrying about 35lbs pack included. Does that seem reasonable?

If your splitting the tents/food/cooking gear 35-40# should be doable.

Yes, it will be split.

I used s 10 degree REI bag in the north Georgia mnts in nov and was good and warm every nite except 1 when the temp went down to 18 degrees feet were cold that nite

I want the bag rated 15-20 below what the actual temps will be.

The GI bags are not all down, but down and feathers. I like them for what they are . I have a Wiggys -60 bag and they built it with the rectangle foot- I can’t stand the narrow bottom of a mummy . Rarely ever use it but it rides in the sled.

Down is warmer and lighter than Poly, but wet down is worthless and wet poly will keep you alive.

For summer camping trips in Alaska you will be fine with any decent brand sleeping bag in the 20-35 degree range. Pay attention to the weight and what they are using for insulation, kids have a way of getting everything wet so I never used down for my kids. North Face, REI, Mountainhardware all make quality lighter weight bags. Once you start talking mountain camping or fall in Alaska you need warmer bags!

I have used the old GI down mummy bag and several Wiggys bags. Both are great bags but what I like to refer to as car camping bags since they are so bulky and heavy. But you should never be cold in any of them

Wiggy has some 40 degree bags that are not heavy on sale right now.

Another reasonably priced option is the current generation military sleeping bags. Its a 3 layer system, using synthetic insulation and they work good. Still bulky and heavy if you use all 3 of the bags together but the lighter weight patrol bag is pretty reasonable and works well in Alaskan summers. You can find them pretty cheap on ebay or military surplus stores, typically less than $100 for the complete 3 bag system.

https://www.amazon.com/Military-3-Piece-Modular-Sleeping-Gore-Tex/dp/B01BFUZXKU

I spend at least a month camping every year and I can give you one tip that greatly improved my sleeping bag experience- buy a liner.
I have an EMS 30 degree, and REI 15 degree and a Big Agnus 20 degree. I really like the Big Agnus but any of them will do fine. A liner will add 10 to 15 to your bag. But the uses are endless. Wrap it over your face to keep bugs or sun out. On a warm night, sleep open bagged but use the liner to keep the cold draft from getting to you. Use it like a sheet when you go in a little dirty or sweaty your sleeping bag won't get all nasty. On really warm nights, ditch the bag completely and just use the liner.
I usually just stuff mine in with the bag stuff sack, its so small it fits in fine.