How do I connect an Electric guitar to a Mac by Firewire?

Question

Please forgive my lack of technical knowledge, I don't play guitar so the terminology is way beyond me. I am trying to find the best (and economical as in value for money) way to connect a guitar to an Intel Mac mini via Firewire port.
My daughter is getting an electric guitar for Christmas (Cort MGM-1) and a Roland Cube amp. She's been playing acoustic for five years already and is very good on guitar (now studying Grade 4). She will most likely want to record her guitar playing into software on the Mac, and I wondered what the experts here would recommend as being worth looking at.
Apple has a few pages given over to this here
http://www.apple.com/pro/techniques/connectingguitar/
which mentions using analogue via the mic input, or digital using an "interface" but the problem I find is they only recommend USB connections, and these are pretty expensive anyway. Still, if that's the price, so be it. I would prefer to use Firewire over USB every time, if possible.
The Roland website says you can connect the guitar directly to the Mac with a cable from the amp, but threads I have read and help I have so far received on a Mac magazine forum indicate the need for a separate "audio interface" and others talk of needing a pre-amp. I am getting confused! Is the Roland amp not also a pre-amp.interface itself?
My budget is pretty low now too (actually it's been exceeded, but I'm aware of the "Buy cheap, buy twice" argument and want to think ahead. Her sister plays Flute and Clarinet and they both sing, if that is any help.
I know there are some really professional and top grade experts on this forum, and I would welcome your suggestions, recommendations and opinions. Please help me work out what to do!
TIA

Answer 1

Thanks a lot to everyone for such a wide range of ideas. I've spent most of the day researchng them, and it is confusing. Now we have a number of options that also include software, eg ProTools or Cubase LE 4 or Ableton or some other program. That means even more research! And won't that double up what we are already doing with Garage Band or Logic? SOrry, I'm just a poor Sax player used to playing the dots, unamplified!
One big reason to go with Firewire (apart from its just better anyway) is the USB ports are pretty full on the Mac IIRC but the Firewire is totally unused.
As for plugging the cable straight in the back of the Mac into the Analog In port, that would only allow a single stereo input or two mono ones, and that could be limiting. I agree though that it would allow for something to be done pretty immediately.
I liked the Shure mic recommendation, I hadn't thought of that but it was extremely useful information which was great for you to add in. Very wise advice. Not sure if its a condensor mic or not, and not really sure why a condensor mic is supposed to be better. They are more expensive though but nothing in this world should be acquired because of price alone IMO; sometimes the minimum cost of something really useful is higher than just the minimum cost of purchase.
When I get one of these interfaces, where in the daisy chain should it be placed?
Guitar - Amp - Interface - Mac
OR
Guitar - Interface - Mac
OR
Guitar - Interface - Amp - Mac
or doesn't it matter?
If it is placed in the chain, should the amp effects be restricted to "Clean" leaving the interface or the software to do the effects, or can you change settings in as many places as wanted? I am guessing this is only a question when connecting to the Mac?
Sorry to ask so many questions, as you can see, I am getting hold of bits of ideas here and there, but there are still big gaps in my understanding. You've all brought me forwards a lot since this morning, I owe you all a great big thank you!
To sum up (please correct me where I am wrong or incomplete) what I am looking for then is an Analog to Digital converter with a Firewire (or USB perhaps) connection to the computer. These come in different flavours, often with "free" software, and can add effects in the computer just like some amps can. They all cost something like £100 to £200 upwards (same price as the amp really) and are in effect "amps for the computer" - or is that totally wrong?
As I said, I value your input and corrections.
TIA