Ditto what the others said - if you record a live band at home without spending quite a few thousand of dollars on equipment and the room, the best you'll get is a third rate sound that may be only just be sometimes listenable (depending on the kind of music).
The cost versus 'improvement in recordings' is exponential: it costs more and more to improve the sound by less and less.
Even if you manage to get some happy sounds onto disk, the biggest problem with home recording remains the mixing and mastering stage. Not only do you need high quality expensive monitors, the room you mix in needs to be acoustically neutral. Without that, whilst you can achieve a great sound in your own mixing room when you play it anywhere else it will likely sound absolutely crap - good translation to a variety of other listening environments and equipment is extremely difficult.
In addition, mixing/mastering takes at least a couple of years of constant practise in a perfect listening environment; you can't improve your skills if you're making audio decisions by simply guessing all the time.
Note that the people who build full recording studios in their garages or garden sheds are not fanatics who are going to extremes with their hobby. They are the people who are doing the minimum toward getting a listenable, translatable sound whenever they record. And if you ask them, they'll still say that they're not 100% happy with the outcome.
Having said all that, if you don't expect many of these recordings to be serious viable listening material or to generate any ROI from them, but instead see it as a way of just having fun and being creative, then I think it is a fantastic idea to buy your kids a thousand dollars worth of equipment and see what they can do with it (bearing in mind that this will get you a third rate sound as opposed to a fourth rate sound, which would basically a stereo digital recorder like a Yamaha Pocketrak in the middle of the room).
If I was in your situation myself, I'd probably buy them a Zoom R16 (400$) and five mics (mixture of sm57s and sm58s) with stands, and let them get on with it the best they can.
Once they've got their happy sounds down onto an SD card, they can:
· mix and mix-down their tracks in the Zoom R16
· Load it into Sonar (my favourite) or Cubase. Abelton is primarily for looping dance music, but they could use that too. Macs have Garage Band, which is also good and very simple.
· Get the tracks professionally mixed and mastered for 50-100$ per song, if they needed it to sound and translate slightly better than the results they achieved by themselves.
Good luck.