We designed our team as an outreach ministry from the beginning. We planned to go on mission trips and perform outside our church as much as possible. We made sure that the kids that participated understood the purpose of the ministry and that they were learning service to God. Make the kids and yourself go though training before they ever perform with a puppet in front of an audience. Also, if they aren't quite ready, don't put them out there too soon. Bad puppetry detracts from your message. Don't accept anything second rate.
As far as where to perform, we performed at other churches more than our church. We worked really hard on developing a professional team with solid puppetry techniques and consistent performances. We used recorded materials almost exclusively. It was rare that we did anything live. We competed in the One Way Street song and skit competitions every year. All the scripts we performed in competition were original (Daniel and Zacchaeus were performed there). We received gold medals in 5 of 8 competitions, both song and skit (song is much harder, more teams competing). This got us a lot of exposure in North Texas and we performed at a lot of other churches based on recommendations that came from that. We were even contacted by a puppet team leader from North Carolina to perform at a Methodist convention in our town because she saw us mentioned in a One Way Street newsletter. One of our puppeteers was noticed by Puppet Productions during one of our performances at a performing arts festival and ended up going on tour with them.
We never charged for any performances. When asked what we charged, we simply said that they could do a love offering if they wanted to. A lot of churches pay what is known as an honorarium, which is basically a set fee they pay for performers to come in and perform for their church. This is also a very good way to raise money for your ministry.