Consider the following:
Budget - In addition to a remote camera purchase, a budget also needs to address other necessary purchases. Do you want to purchase everything at once or will you have to spread purchases out over a few years? What are you wanting to do? - just be able to control the camera and push the picture and sound to another building or make the viewing experience "as good as General Conference"?
Quality - The quality of the camera image is the most important factor in the overall presentation. However, if the rest of your system has issues, you will negate the camera's quality. For example, all of the following play a significant role determining how good or bad the picture on the receiving end is; improper cabling and/or distribution, a cheap capture device, building distribution (RF) problems, inferior Internet bandwidth, poor quality projectors or monitors which are not adjusted properly (or downright defective), lighting that washes out the picture, etc. Why spend a significant amount on a camera and not address every factor in the broadcasting chain? Evaluate what you have now and what needs to be addressed or fixed. You can do this with the resources you currently have and go from there.
Zoom Ratio - Where do you plan on positioning the camera? If it is in the back of the chapel, a 12x or less will result in lots of distractions from people seated behind the speaker still being in the picture. If you can get 18x power or more, you will be able to crop out heads and only have a head-and-shoulder's shot. Only consider optical zoom ratios as digital zoom is not useful.
Control - Various camera's control systems can be anywhere from useless (it may have a fixed optical lens and only a grainy digital zoom) to professional, I hope you don't don't think that just because a low cost security camera is PTZ, it is a good choice. Consider additional benefits and features (such as servo control - graduating adjustment control) and operating more than just PTZ control such as color adjustment (to match the color of multiple cameras), overriding focus (when automatic will not work), iris (our chapel's white wall is TOO bright), etc.
Format - Analog composite video has been just fine for decades and if a system is done correctly, can achieve professional results. If you are investigating HD component or HD HDMI or HD-SDI, then the rest of your equipment will need upgrading as well. If you really want to do a HD broadcast, every piece in the system will most likely need upgrading...so just add a zero the end of your budget figure. Ask yourself if anyone will appreciate it? Will anyone REALLY notice the difference?
The church recommends the Sony EVI-D70 as their suggested remote controlled camera, and I agree. It can be controlled right out of the box with an I/R remote, but also with a computer or with a remote control box (remote joystick control). I currently feel that there isn't a much better product out there for the money. The Sony has great PTZ servo control capabilities and just about every single setting can be controlled remotely (servo pan, tilt, zoom, focus, color balance, detail, iris as well as shutter speed, white balance settings and on and on). The camera is perfectly matched to Sony's RM-BR300 servo joystick remote control box and up to 7 of these cameras could be controlled from the same unit. The camera's zoom ratio is 18x which if placed 75' from the pulpit (back of the chapel or chapel overflow), you can get a great head-and-shoulder shot and crop out the distracting background with a little extra optical zoom left over without getting into digital zoom. On the down side, it is only 470 lines (resolution) and the supplied I/R remote has very limited features. It also can tend to blotch colors on diagonal objects (purple or yellow on the rim of the choir seat).
The AZ Gilbert Greenfield Stake has been using Sony EVI-D70 cameras for several years now. Even though this a low-end camera (as far as video quality), the PTZ features have made it a perfect choice for remote, hidden operation. Instead of upgrading cameras, I chose to work on improving the quality of the system as a whole. So now, even with the Sony EVI-D70 cameras, we get comments like "It was just like General Conference"