Get a committee together as soon as possible. They can start out by electing officers and maybe even filing for the non profit status. I am not sure about that, we did it right away so that we could solicit donations.
Then have a meeting and invite all the local families. Perhaps a block party where someone supplies the meat and someone else supplies the paper goods then everyone else brings supplemental stuff. Or you could just do pot luck. Get everyone motivated by your best speaker. The one who can sway them to get behind the movement.
Then you are ready to start your project.
You have to get approval from the city first and foremost. They may have plans to build one in your area already. We built a skateboard park and BMX track in a local park. They leased the land to us for something like $100 for X amount of years.
There were lots of companies that would donate stuff to us because of having the city approval. We got all the dirt for the whole track donated by a local sand and gravel company. We also got the city to put up lights and public bathrooms. It turned out really nice and we have it as long as we are operating and using the land. If we stop using it or let it go to seed, not take care of it by not mowing, letting the grass die, etc....then it reverts back to the city and they can tear it down or use it. Their discretion.
So getting the city on board in momentous. They could even have a place on the board/committee that way zoning laws would be a snap to get through. They would already know the laws and could tell you if it's a bendable one or an iron clad one that you'll just have to do it their way or not at all.
Once you have the go ahead and people willing to work start calling companies you can find online. Here are some ways that I would divide the work load. The ones who like to beg on the phone for donations can do some, others can do their best stuff too.
Google grants for community playgrounds.
Call local banks and find out if they know of any grants out there.
Call local charity organizations to find out what grants they accessed to get funds for similar fund raisers. Head Start may be a good one to call. Find out if the local child care centers have any leads of grants. I got one for almost $10K to remodel my playground years ago.
Get your local sand and gravel companies to commit to donating at least one truck load of sand each. That way none of them are overtaxed by the donation. Be sure you don't go with pea gravel in your sand area. It's hard on feet and gets in shoes, it's just not fun to play in. It is okay to fall on it in the fall zone area but not to dig and play sand castles in.
Get some companies that sell playgrounds to give various quotes. Get dimensions and depth you can go. These companies will have playgrounds from a few thousands up to hundreds of thousands. Why not have several options to select from if you get the funds you hope to have.
Here are some links to play ground equipment:
http://www.world-playground.com/daycare.htm
http://www.imaginationplay.com/assets/images/Entire_Imagi...
http://playworldsystems.com/
http://www.spencercreekrec.com/daycare_prek.html
http://www.kaplanco.com/outdoor-play-equipment.asp
This one has some interesting concepts for outdoor play, handicapped and other stuff too in case that is something you have to include.
http://www.childcaredepot.com/productCat0.ivnu
Make a wish list of things you want to have. I would like a pool too but as far as money goes, who knows what you will end up getting.
I would include things like tables and benches (city may provide these), climbing equipment, sand box area for digging, balance areas, rock climbing wall, towers, jungle gym, all kinds of things like this. If you get a basic structure you can always have ongoing fund raisers and add to the structure too. If you have a slot that is open then you can buy an addition and put it there. Each year you can add something or take something away that is outgrown. The President of the organization will have to figure out where to store the stuff you take down though....
Have fun getting everyone excited and moving forward!!!!