The Featured Image field is not designed to display a poster or flyer or any image containing text. The details which are on your poster should be entered into the Description field.
It's important to choose the right media and format for the right medium.
A poster is designed to be print based.
An image of a poster is not appropriate to display on the web.
Images cannot be read by screen-readers, and PDFs do not scale well within a web page.
The Featured Image field on Services and Events is there to display a nice landscape orientated image to represent and complement the Service or Event details. It should contain no additional information which isn't otherwise already included in the Description.
Here are some examples of how a church has used the Feature Image on their Services and Events:
Different churches have different sources for their photos.
Some take their own photos and use those.
Some use stock photos.
These two articles may assist you in finding and selecting photos: