Here is the not so definitive SOP on what you need:
I have lugged carry bags, shoulder slung bags and carried enough I looked like The Jerk going down the road with the airport bag on wheels. Here is what I have learned, take it or leave it. My total pack weight is 55lbs.
1. Back Pack hiking style internal frame $80-$90.00
inside pack: 3 pairs of cargo pants ripstop (14.99 at Walmart, 3.99 Good will), 3 Cotton T-Shirts (dark color not black), 3 pair boxers (you need the air there), 1 large size Ziploc bag with toiletries (neosporin, 1/2 roll Toilet Paper flattened, and band aids too!), Cotton or wool socks at least 5 pair, One sweatshirt (I carry a reversible wool / waterproof jacket for this item), Laptop or other loose item that is important.
2. Sleeping Bag 30 degree rating w/ stuff sack attached under back pack with thin blanket inside (blanket helps with when it gets below zero, stuff underwear and other clothing inside when other insulation is needed!). Walmart $15.00
3. 2 person tent, preferably one that the entrance flap goes all the way to the ground to prevent wind and critters from gaining entrance. ($30-$40.00) cheapo walmart no more than 4lbs. weight!(15.00 without down flap)
4. Hiking Boots! You need good boots! I cannot stress this enough. You are out of action with a twisted ankle. Boots at Goodwill are $5.00! Good thing to advertise on your Pan sign you need. Goodwill is the Wanderingvets best friend!
5. Personal Hygiene Kit Tooth Brush, Tooth Paste (recommend Tom’s of Maine) Dental Floss (not only for flossing, for clothes line, and stringing rocks in cans around campsite in urban areas), Plenty of Band aids (a lot of heel blisters) neosporin, cortisone cream, cotton swabs, Listerine (mouth wash yes, but very antiseptic also for cuts), deodorant (pits get stinky reccomend DEGREE), Razor (Mach3 works best), soap (Pears), nail clippers (keep them short to keep bacteria minimal), Anti-diarrhea tablets (you do not want the runs) At a dollar store this list retails about $11.00
Bring extra Ziplocks and garbage bags for waterproofing! pack everything in plastic bags. I also carry plastic tarps for plastic tents emergencies!
You just said sarge you left out food, utensils, my PS3, winter clothes, and my dog Spot! Well the utensils come in plastic from any fast food places, get all the condiments you want! If you want to spend the nights with the game boy, maybe you should have put that down a long time ago! The seasonal wear like coats and mittens you get at the good will or salvation army. Remember, go to the ones in the richest part of the cities that you are in! That is where the designer loot is for the lowest prices. Brand names like Eddie Bauer for a buck you cannot beat it. This is light survival like the light infantry, you can take what ever you are willing to hump a long with you. But troops there will be days you will not get a lift from anyone and so it is important to keep the weight down since you are carrying your home on your back. My pack weighs about 55 pounds. That is heavy but it keeps me alive and comfortable at night. It is neat and orderly also and people ask me if I am a HIKER not if I am HOMELESS. There is a difference in peoples eyes. It is a in outward appearance that we are unfortunately read dear Vets and Friends.
Wanderingvet
Stumble It!
Wanderingvets.com 
Do Not Buy Any ACADEMY SPORTS MAGELLAN PACKS!
Also, do not buy the military surplus gear. It is way to heavy. The military gear is built to be transported to carried. The only piece of military gear I carry is the rain poncho.
For in the Cities it is ok to use the scented products but do not go too strong on scents.
In the woods always use UNSCENTED products in soaps and deodorants. It keeps the animals away and unaware of you.
When you’re homeless you may not have this guys money to spend so I recommend Ivory soap bars as they’re both the cheapest and they have no scent, any mainstream toothpaste is fine since Toms of Maine is pretty spendy and taste bad (to me at least) not to mention that they used to use aspartates (which are excitotoxins, yeah that’s a real word, look it up) and though you normally have to take a lot of them many vets are chemically sensitive due to their service in Iraq. Mach 3 razor blades are spendy compared to any quality 2 blade razor with a lube strip, deoderant of course is up to user but don’t use anything that lists “aluminum” in any of its many forms as this is also a toxin. Ziplocs can often be found on the side of the road up here in Seattle and simply washed out, trash bags are ok and pretty cheap but the “contractor” bags are much thicker and last a lot longer, try a construction site and ask for one or two, heck even ask for some visqueen, I often can get one or both from the workers there as long as you’re friendly. Backpacks are nice but pretty spendy and don’t last very long, I recommend either buying an exterior frame pack at a thrift store or getting your duffel bag out of the closet before you get kicked out, you already know how sturdy that thing is and since you shouldn’t be caring more than 30-35 pounds you’ll be ok, yeah I know he carries 55lbs but that’s 1/3 of my body weight and is a real pain that I don’t need. I do just fine with less weight since I simply scrounge more stuff up regularily and since I also maintain a “rainy-day fund” it’s not a problem to replace something quickly if I can’t find it free elsewhere. Don’t buy Keen brand boots, I just got done destroying a pair in less than 6 months and for the money they were comfy but just didn’t last, Army basic boots are ok if not very well padded and the padded band at the top really grinds into my calves (I’m short and have thick thighs and ankles) which leads me to my next point: buy loose clothing but don’t buy cargo pants (or at least GI ones) since they make you stand out (not in fashion anymore) thus you look like you either don’t know better or are a homeless vet! Unless that’s the look you’re going for. Ah well running out of time here, it’s a pretty good site and I appreciate a chance to let off a little steam and help out with my advice. Thanks, Mike
May I suggest a cookpot and a small propane/butane canister stove these are cheap at sporting goods store buy your fuelcanisters at wallyworld $4 coleman brand 7oz lightweight fits easy into a pack and GR8 4 urban areas and Anywhere else campfires Will attract unwanted attention this will help stretch your food dollar in lean times canned & boxed goods are quite cheap at discount retailers and these make GR8 hand n feet warmers in a pinch though use Caution