My solution but not uniquely my idea. Create economic refugee camps on abandoned military bases and other similar locations. Build/renovate military style barracks housing, on site day care facilities, kitchens, etc. Focus *all* government, religious, medical, mental health and other charitable aid and volunteers on these camps. Your church want's to feed the homeless — donate money and/or come volunteer at the kitchen etc. The day care facilities can be partially staffed by camp residents who are willing to do the job so that others can go out and find work if they wish. Maintenance jobs etc, can also be staffed by those who are willing to do the work (and get paid). All properly supervised by proper professionals.
Sweep the streets clean of any and all panhandlers, homeless people, urban campers, etc. Everyone is taken to one of the local economic refugee camps where they are guaranteed subsistence level living - safe place to sleep, sanitary facilities and basic nutrition. If that's what they want — to simply exist — then they are free to do so at these camps, no hassle and no questions asked.
If they don't like the subsistence level living in the camp, then they are free to go get work or find other arrangements. The camp gates are never closed and never locked - but they will NOT be allowed to live on the streets, parks, sidewalks , etc. Anyone found there will be summarily returned to the camp.
This keeps the streets and public places clean, provides subsistence level existence for those who seem to want it and a chance to do better for those that do not. It focuses all money and aid in one place for economy and efficiency of scale, instead of a thousand individual efforts scattered all over.
This is a broad overview — but it's probably already too long...