Hi yepbuddy! Welcome to Talkbass...
I've recorded a church choir using my laptop and audio interface. I can give a short answer here but if you want to discuss specifics then please send me a personal message (PM).
First you will probably need a computer. Laptops are good and portable and can be brought into the church and taken away again for security as required. And hey! You can use it at home too!

There are one or two specs of the laptop that are important - one is the amount of RAM: 512Mb is a good starting place and most laptops have at least this much nowadays. The other is hard-disk space and speed. Audio takes up a lot of room: about 5Mb per minute of mono at CD quality. Now if you've got 8 tracks or 16 tracks then simple maths will show that you're going to need a fair sized hard-drive. The hard-drive speed dictates how many tracks of audio you can record to at any one time. Faster drives sustain higher data transfer rates, and so you get more tracks running simultaneously. So, for starters try to get at least 60Gb+ space and 4200rpm+ speed. The speed of the processor is important when it comes to number crunching the audio - faster chips get the job done quicker and can handle more effects simultaneously. However I've put together tracks on a 600Hz Pentium II with 512Mb RAM so by today's standards your going to be doing pretty well any way you choose. HOWEVER, Pentium IV's produce a fair amount of heat and when the fans start whining they can cause disruption to recordings. And be quite irritating. Centrinos or Pentium M class (same thing) are pretty nice and run cooler. Pentium M seem to offer slower performance, but if you multiply the number you see by 1.5 you're getting close to the equivalent Pentium IV, viz: A Pentium M 1.7Ghz will be close to 2.6ishGhz Pentium IV. Battery life also tends to be better with Pentium M and Centrinos. Screen resolution can also be an important factor - more acreage means that you can view the full mixer when recording your tracks and so you won't have to scroll around the screen to see what the drummer's levels are!
Audio interfaces come in a wide variety of types now. Firewire interfaces are faster than USB devices (except USB2 but they're rare at the minute). Firewire will offer something of the order of 8-10 tracks of audio recording simultaneously at CD quality. USB will offer 4-ish at CD quality. There are differences as well in terms of latency - the time it takes for the audio to go from the inputs on the interface to the outputs having gone through the PC. You can get Firewire interfaces like the Firepod which has 8 mic inputs. Very handy for choirs and church bands. You can run the inputs straight off the mixing desk. There are some other audio interfaces which allow you to chain together multiple inputs to increase the number of channels you can simultaneously record.
Usually if you record choirs and musicians you may need to record sub-mixes from the mixing desk so that you get down to the 8 or 10 channels your audio interface allows. This still leaves some flexibility in mixing after the event.
Software is a matter of taste. I can only really recommend downloading demos of certain programs and see how you like them. Cubase and Cakewalk Sonar also work with MIDI notation so you could use these to score pieces, produce chord charts and also to record the works themselves. Other software like Adobe Audition is purely audio recording, but does that very nicely.
For laptops, it's usually better to stick to a reputable brand - Dell, Sony etc. since these tend to be more foolproof when it comes to connectivity - but it's worth checking with a retailer whether the laptop you're thinking of will work with the audio interface etc. Check on user forums for the different brands. Audio is a finicky business sometimes on computers since it places high demands on the system for uninterupted transfer of data. Some laptops are more geared towards surfing the net or fragging newbs in some shoot-em-up game. There are also machines specifically spec'ed and built for audio but these seem to carry an extra premium in cost.
For audio interfaces, many come bundled with software. The Presonus Firepod comes bundled with a version of Cubase SE.
The next port of call: Try Sound on Sound for great advice on recording to PC's from Martin Walker.
http://www.soundonsound.com/ Computer Music is more geared towards folks producing "dance" / loop-based music, but has a cover DVD jammed with software demos, tutorials and WAV loops.
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Hopefully now the FAQ in this forum may start to make a little more sense... Check out previous threads here around Firewire interfaces. Several other folks have been thinking along similar lines.
Welcome, have fun, hope you get up and running soon!
Mike