People have used condensor, dynamic and ribbon mics for micing guitar cabinets. The classic is the dynamic
Shure SM57 on a short mic stand almost up to the grille cloth in front of the speaker. You can experiment with the placement of the mic off-centre of the speaker for different tones and speaker colourations.
Shure tips
As far as an amp goes, the classic rock guitar sound is made by overdriving the amplifier to the point where the sound is compressed and clipped and eventually totally distorted. Therefore, if you get a 120 W amplifier, the sound levels will be thunderous to get the distortion and drive that is desired. Many guitarists are getting "mini" amps - 2W to 10W - for recording, because they can be cranked up to get that "creamy" sound without risking building demolition. (Many of Brian May's characteristic guitar sounds on Queen records were recorded through his "Deaky Amp", a tiny amplifier hand-built by John Deacon, Queen's bass player) Solid state amps and vacuum tube amps have different characteristic overdrive and distortion sounds, as do variations between brands, speaker sizes, etc.
Major page on
amp tone
Tweakheadz
Digidesign
Guitar Tools article
The other way is to avoid the use of an amp altogether, and use an amp simulator effect - which creates the overdrive, speaker colouration, and other effects electronically. The Line6 Pod series, the Behringer V-Amp, Korg Pandora, Digitech GNX series, Zoom, Boss/Roland COSM, and others are popular. They will give you a line level signal to pass to the recording interface with no amp, speaker or microphone needed.