The most challenging part of getting your church service online has more to do with your content preparation than anything else. There are numerous streaming providers, some free some not, and even more hardware manufactures to choose from. Just about any combination will get you online and streaming but it's how you prepare your content that will really make a difference and give you the best results. What I mean is this; the better the content upfront, the better experience your audience will have. 

First, audio should not have a huge dynamic range. It should not be too loud or too soft. You don't want your listener to constantly have to adjust their volume.

Second, your video needs to be the highest possible quality as well. Streaming video doesn't look great to begin with so if you start with poor quality video you will end up with really poor quality video. Take time to get the cleanest signal possible.

Third, be careful to remember the context in which your audience will experience your service. A person watching your service in a 3 inch window on their computer screen won't be able to see much detail unless you keep your shots fairly close. So, pay careful attention to your composition. Closer shots will also help reduce macro-blocking.

These three principles may seem basic, but if you follow them you will be successful at delivering a streaming experience that your audience will enjoy. This is the foundation, everything else is just icing on the cake.