In most cases rather than using a laptop I'd recommend just using a pocket camcorder
to record the services for later viewing. But since your wife wants a new laptop anyway, what you are asking is indeed possible. I exclusively recommend ThinkPad
laptops, specifically the T-series, L-series or Edge models, all of which are available with integrated webcams (make sure you choose a sub-model that has one).
You could use Skype via the laptop to see the services live, or you could record and watch them later. Even with a built-in webcam, I'd recommend getting a high-quality external webcam like the Logitech HD Pro Webcam C920
, which will offer a much better picture and sound, plus the ability to easily point the camera in the direction you want (without having to aim the entire laptop), and it includes easy to use recording software as well.
If you are on a budget you can get ThinkPads on a discount via the Lenovo Factory Outlet store