both applications will create excellent video (assuming source is good quality). The question is learning curve. I would recommend demo'ing both products and go with one that "feels" better. I use Sony's Vegas.>Also - the sound quality on our video recordings isn't that great. How and What do we >need to do to record the sound straight from the mixerboard to the computer
Console to computer is a wide open question. It greatly depends on the console and the operator. Most often a sub-group or matrix is assigned on console that is directly connected to the computer's sound card. I recommend the use of a usb or firewire connected sound card. I have found he powersupply some laptops will back feed into the main console and definitly in the recording. Also, use a ground loop isolator ex. radio shack Model: 270-054 to keep the signal path clean. At that point you can use whatever audio caputre application you like or you directly stream the product out with Microsoft Media Encoder or some other live encoding software.
The quaility of your mix will depend greatly on how you setup the console. if you choose to use a matrix you may not like your mix as it is copy of the live mix. This mix generally is not suitable for recording music becuase is mixed specifically for that room. if you use a sub-group the engineer may not have the time during the worship set to dedicate to your sub-groups mixing requirments. Best choice is a seperate console for mix the recording, this however is not always practical nor possible.
troy