For sound, I recommend starting with pre-recorded scripts and using a nice boom box. That's how we started and we now have a full sound system with remote mikes. It took us at least 5 years to work up to it.
Funding generally comes from getting sponsors in your church, having garage sells, working concessions for special things held in your church. We also raise money through performing for special functions at other churches (as well as selling stages, CDs, patterns).
I hope this helps. This information should be enough to get you up and running in short order. All it requires is time and commitment (and a little funding never hurts).
We have performed in parks, apartments, and other outdoor venues. That's why I designed our stage the way it is. The main thing to watch outdoors is to always make sure the audience is lower than the top of the bottom tier of the stage. This is so that no one sees the actual puppeteers.
Sound doesn't travel well outdoors. A boom box will only get you about 30 ft beyond the speakers. Anything farther than that and the audience either won't be able to hear it or won't be able to understand it. We ended up purchasing a sound system that has 250 watt speakers. You can hear them a mile away.
Most parks have electricity but you always want to check into it ahead of time and make sure it's on. That usually requires a call to the parks department. Always have about 200-300 ft of cord on hand and a power strip in case you need to power multiple things.
Take a painter's tarp and some old carpet to place on the ground beneath the puppeteers. You will only have to put your knee down on a rock one time to know why the carpet is needed. It hurts a lot. The painter's tarp is usually pretty large and gives you a place to set your puppets down with out getting grass and dirt on them.
Always face your stage toward the sun and put the back of your audience to the sun. This does 2 things, it prevents backlighting of the stage and performers which results in the performers being seen through the curtains, and it prevents the audience from looking into the sun and squinting instead of watching the presentation. Shady spots are ok, but the difference between the light and the shadow may make it difficult for the audience to see you. If you have to make a choice, put the audience in the shade.