OK- I will try to break down your question to its fundamental components. I will presume you mean an electric guitar, but the signal chain for an acoustic is not that different. There are 2 commonly used ways to do it:
Plan A- This is the one recommended by most experienced audio engineers:
guitar > amp (usually a smaller one than is used for most stage work) > one or more microphones (a stage dynamic such as a Shure SM57 is often used, sometimes in combination with a condenser mic) > microphone preamp (this raises the weak mic level output to line level) > A-D (analog to digital) converter (this changes your analog signal to some form of digital output that can be recognized by the computer. In the case of a laptop, this is likely to be transferred by USB, firewire, or S/PDIF) > audio software for processing (there are tons of them-soundforge, reaper, audacity, N-tracks, etc.).
Plan B- DI (direct insertion)- This is not the first choice of most engineers, but has become more popular as the technology for doing it has improved:
guitar > specialized preamp or "DI box" which changes the instrument level output to line level > A-D convertor > computer by USB, firewire, S/PDIF, AES/EBU etc. > audio software for processing.
OK- now that the specific components have been identified, we need to break it down into the actual hardware. Generally, only the big time studios with pretty deep pockets are going to have every component a top of the line separate unit. You could spend thousands on a preamp by itself, on an A-D converter, or on certain microphones. That isn't the starting point for most people in the real world. For most of us, we use devices which are less expensive, and combine several functions of the units above.
Some mic preamps have the A-D convertor built in, and provide digital output. Mixers are really just a bunch of preamps with multiple signal routing options. Some of those have digital output also, but most don't. An audio interface, which is commonly used, is basically one or more preamps with a built in A-D convertor, and usually a built in DI box for direct instrument input. The specialized preamps I mentioned above usually contain guitar amplifier modelers, which use digital processing to simulate the sound of certain amp and cabinet combinations, and contain digital effects as well, such as reverb, delay, flange, compression, etc. Many of those also have an onboard A-D convertor, and provide digital output. In some cases, a DI box or audio interface is used, and the amp simulation/effects are generated in the computer by software, such as amp farm or amplitude.
Now that we have defined the parameters, what are the advantages and disadvantages of the various options?
Plan A has the advantage of being similar to the system used for recording guitars for 50+ years. We have become used to the sound of air pushed by a speaker hitting a microphone, and it is the most straightforward way to translate the amp sound you know you like to a recording. The biggest problems are that a cranked up amp makes a lot of noise, and learning where to place that microphone to get the sound you want can be a major pain.
Plan B has the advantage of being quieter, and more portable, and allows you to dial in many different sounds, including vintage amps you don't own and probably can't afford. Its other main advantage is that it deals the room out of the equation, so you can do it in a room with poor acoustic properties and lots of background (ambient) noise, which tend to be picked up by microphones. The main disadvantages are that finding the right settings to get the sound you want is a pain, and it simply doesn't move air that smacks a microphone. When done well, direct recording can work, and a lot of commercial tracks have been done that way. Critics of it, and there are many, will tell you it produces a dry digital sound which does not compare to a cranked up, mic'd up tube amp. Another variation on the DI approach is to send a line out from the amp (assuming it has one) directly to the preamp or interface, so in other words, the amp has a built in DI box.
The quality of sound you get in the end is a factor of the quality of the instrument, how well it is played, the room (if mics are used), the quality of the preamps, the quality of the A-D convertor, and how well all that equipment is used.
When choosing the actual hardware, aside from your budget, you need to determine not just what your present needs are, but what your future needs will be. If you get a simple DI guitar rig, you may decide later that you want to record vocals, or drums, or whatever. Then you need mic inputs with multiple channels of preamps. Also, the number of channels you can simultaneously record and process is a function of what kind of inputs and processing power the computer has. For more than 2 simultaneous channels, firewire is usually used, and for 1 or 2, it is usually USB. Sometimes a mixer is used to pre-mix or sum a bunch of inputs, usually multiple drum mics, which are then sent to the interface as a single signal. This gets you more inputs, but you can't change the mix afterwards or process the individual signals separately later.
You also have to take into account how you will hear the music, first when you are playing it, and later, when you are playing it back. For pure DI, you'll need to listen through headphones, and for playback, most interfaces have an output for powered studio monitors, which are not unlike powered computer speakers, but more accurate, and can be pricey as hell.
Alright, I've thrown out the concepts, now it is time to get down to actual hardware. I'm not even going to talk about expensive component rigs. If you were ready to spend thousands on this stuff, you would have asked a different question in a different forum.
mics- The one most commonly used is a classic standard stage mic:
http://www.8thstreet.com/product.asp?ProductCode=1361&Category=Microphones
I happen to prefer this, but that's just me:
http://www.8thstreet.com/product.asp?ProductCode=3202&Category=Microphones
Simple USB interfaces: There are bizzillions, but these 2 are used by a lot of satisfied customers. Both allow you to use mics or direct instrument input. The Line 6 unit is a little specialized for guitar, and includes amp modeling and effects:
http://www.8thstreet.com/product.asp?ProductCode=60669&Category=Audio_Interfaces
http://www.8thstreet.com/product.asp?ProductCode=40819&Category=Audio_Interfaces
OK, you just want a simple guitar interface? This is cheaper, but doesn't do microphones,and has limited monitoring options. so is much less versatile:
http://www.8thstreet.com/product.asp?ProductCode=22562&Category=Audio_Interfaces
Need a bunch of channels for future options? Consider:
http://www.8thstreet.com/product.asp?ProductCode=32675&Category=Audio_Interfaces
Want to add a mixer for drums, etc.?:
http://www.carvinguitars.com/products/single.php?product=S16
Headphones- I like these:
http://www.8thstreet.com/product.asp?ProductCode=10952&Category=Monitoring
More advanced amp modelers with digital output:
Cheap and effective:
http://www.8thstreet.com/product.asp?ProductCode=20204&Category=Guitar_Effects
Not so cheap, but an industry standard:
http://www.8thstreet.com/product.asp?ProductCode=22256&Category=Guitar_Effects
In conclusion, if you want my best choice for your needs, I would probably get a Shure SM57 and a short boom stand,
a line 6 UX2, and a pair of Sennheiser HD280 headphones. That will allow you to try mic'ing guitars, DI recording, and amp modeling in a simple USB powered format.
Best of luck. Hope all that helps.-Richie
