At church, you should never split a signal from the computer, you should be running a multi-display system that allows the person running video to organize and view what is going on before being sent out to the projector, you can do separate formats and resolutions. There really isn't any added cost to do this anymore since pretty much every mac or PC from the last decade should allow you to do it. However, even if you did split the signal like you are mentioning (you SHOULDN'T!) the projector or monitor should be able to scale the resolution accordingly if you choose a different one. Personally, I would choose to go with the projectors native resolution and let the computer monitor make do.
As for what format to use, you have to pick whats best for the church, if you are displaying words for worship, I have found that 4x3 is the best but some have just gotten so used to widescreen, that is what looks best to them now. However, if you ever do widescreen video clips, than you can make the argument for a widescreen projector, they have certainly gotten cheaper recently but the classic XGA - 1024x768 projector remains the king for low cost and super high brightness.
Brightness really is the most important factor in determining what projector to get, you really need something that is as bright as possible, I have found that around 5000 lumens is the sweet spot, going much above that starts to get super expensive per additional lumen of output. Have you looked at the Eiki EIP 5500? It is a 5500 lumen PJ from a very solid manufacturer for about $1300 with XGA resolution. If you want a bit more brightness, you can get a Sharp XG-PH80XN, 6300 lumens for just under $2k. Your screen size really plays into things more than anything though, most smaller to medium size churches have something around 90x120 screens or bigger if there is only one of them. I would say you should find a projector that gives you at least 75fl on the screen, you may be able to go down to 50fl if you have to but 75 gives you more visibility with ambient light, it is hard to get enough brightness in a light room at church.
As for what format to use, you have to pick whats best for the church, if you are displaying words for worship, I have found that 4x3 is the best but some have just gotten so used to widescreen, that is what looks best to them now. However, if you ever do widescreen video clips, than you can make the argument for a widescreen projector, they have certainly gotten cheaper recently but the classic XGA - 1024x768 projector remains the king for low cost and super high brightness.
Brightness really is the most important factor in determining what projector to get, you really need something that is as bright as possible, I have found that around 5000 lumens is the sweet spot, going much above that starts to get super expensive per additional lumen of output. Have you looked at the Eiki EIP 5500? It is a 5500 lumen PJ from a very solid manufacturer for about $1300 with XGA resolution. If you want a bit more brightness, you can get a Sharp XG-PH80XN, 6300 lumens for just under $2k. Your screen size really plays into things more than anything though, most smaller to medium size churches have something around 90x120 screens or bigger if there is only one of them. I would say you should find a projector that gives you at least 75fl on the screen, you may be able to go down to 50fl if you have to but 75 gives you more visibility with ambient light, it is hard to get enough brightness in a light room at church.