Sound system board into PC...

 Ok I need advise with this pretty quick like. 
I run the sound for our church and we are looking to get a little more advanced in what we do. Basically what we want is a system that is dedicated to handling our audio from our sound board. From it we want to record things like sermons but also singers. And be able to easily manage the recorded audio (very little editing outside of maybe some minor cropping) and burn to CDs.
My question here is more of a hardware one. First would a desktop tower PC be better than a Laptop to pip the sound into? Here is our board we use ... Allen&Heath ZED24FX .. I have attempted this on an older laptop (single core processor celeron) and the results were... less than desireable. I have been told that its nothing that a computer with a multicore processor cant handle with relative ease. The reason I ask about a desktop is there may be better options for ausio inputs other than USB. The USB on our board is 2 way, but not at the same time so that puts a limit on the convenience of doing things exclusivlely from PC. In other words, if there is a singer, we cant playback their music they sing to AND record them singing all from just the USB cable.
Any help on this is appreciated :)