Hi Judy,
I don't think any of us who chose to be a church organist really prepared ourselves for it. I know I didn't as I was "gently nudged" by my parents when I was but 12 years old. I was in my first year of organ study (after 6 years of private piano lessons) and the pastor's wife became ill and could not play for the upcoming weekend service. I was 'volunteered' as it were, successfully played the service and promptly was accepted as an assistant organist playing every other weekend.
Ready or not, there I was leading the hymns and liturgies - It just happens and we all have gone through this nerve wracking first time experience.
As for mistakes, even the best organist is bound to make an obvious error at some time or another. Try as we may, we are still human and not robots. Recordings can be 'doctored' to remove mistakes ... live performances can't. As a professional musician myself, I choose not to laugh when hearing other's mistakes as I know how much effort goes into the preparation and presentation of any piece, be it a fast and furious toccata or a quiet slow meditative one. Sometimes, those slower quiet ones are more prone to errors because any mistake shows up like a sore thumb.
You might try to get your foot in the door by playing an offertory or prelude piece sometime. One never knows ... it could develop into a rewarding career as a church organist. At some point, one has to just jump feet first into the situation and make the best of a first impression.
When I moved to Arizona in 1982, I was a complete unknown here ... nobody knew anything about me or my talents as an organist. In a way, I had to "prove myself" all over again, as part of the audition for my present church position was to play for a service with the minister of music present. Same thing happened when I left this church (just for the change) to play for a very large RC church with a 94 rank Allen organ - my audition was to play for the Saturday 5pm Mass. I had never in my life played a Catholic Mass, but I made it through that most nerve wracking experience and became their senior organist.
Returning to my original parish a few years later (I've now been the organist at the Lutheran church for the past 25 years) I was accepted back without having to interview or audition - my reputation followed me and I have become one of the top church organists in my region.
So, just put your best foot forward and jump right in if you are ever given the opportunity. You won't regret it.