A backpack is almost a necessity for a homeless man or woman. Especially if they are traveling. They allow a person to comfortably carry their belongings from place to place. Also, if you are providing sun showers (4-5 gallon) then a backpack is a great way to transport that back to camp full of water for a shower.
Backpacks can be purchased at garage sales, thrift stores and flea markets as well as on sale in the store. This is not something that you have to pay full price for since they are so readily available used. The kind your kids use for school is fine. You almost can’t go wrong.
Prices in the store are from $8 and up so used they would be very affordable. Just keep a supply in your trunk and when you talk with a person and feel like they might need one then provide that to them along with a survival guide and a New Testament.