Not talking live sound here...just recording. I've done a lot of experimenting with recording amps over the years. So I'll share some general propositions, and then talk about a few mics I really like to use when recording amps. I say "mics" because there is no such thing as a "best" mic; there are choices that will depend on what one is trying to do. But I do have a few favorites.
First a few general things:
"Why doesn't my amp sound like it does in the room?" -- Because unless your ear is two inches from the speaker, you're hearing the room with its modes, reflections, reverberation, vibrating walls, the floor, etc. If you want to hear the room, mic the room!
Also, a mic doesn't hear like your ears do. Not only is the frequency response different, not only do mics and mic preamps have factors that will alter/distort the sound, you have two ears. Try stereo. Move the mic or mics around. Try different things. Don't be lazy! This stuff takes time, and you have to learn your room. Also, mics have patterns that they pick up. Most do not hear omnidirectionally like you do. Though some mics do. In addition, even omni mics' frequency response will vary from front to sides to rear.
"I'm hearing buzzing sounds. Something is wrong with my amp." -- Well, more likely, your lights, your furniture, the metal vents for your heating and cooling system, your floor, your walls, a hinge on the door, are vibrating sympathetically with certain notes. It often sounds like it comes from the amp. This is structure-borne vibration. You can reduce it by putting the amp on one of those Auralex platforms.
"I get too much/not enough bass." -- Room modes. An amp on the floor will get what is called half-space reinforcement from the floor reflections, that will increase the bass. An amp near a wall gets reflections from the wall and the floor, what is called quarter-space reinforcement for even more bass. An amp in a corner gets eighth space reinforcement, most bass. Experiment with placement, move the darn thing around. If you're getting too much bass, put the amp or cab on a stand or a chair. Etc. Remember that bass is omnidirectional, and high frequencies beam directionally. So highs are less likely to reflect unless they're directly pointing at something, but bass goes everywhere - walls, floor, ceiling. The cab's distance from these surfaces affects how much is reflected!
Room doing too many weird things? Try gobos to isolate the sound more.
"Invest in the mic or the preamp?" -- The transducer is the thing that converts sound waves to electrical energy, and vice versa. That would be a mic or a speaker. The transducer makes more of a difference in recording than the electronics. You will hear the tone of a different mic immediately. The difference between preamps is far more subtle. Go for the mic first. Then deal with the preamp if you're unhappy. Caveat: ribbon mics need to see higher impedance than some preamps will have. If you have a ribbon mic, you need to read your manual carefully, and make sure your preamp has the right specs.
One more thing - mic placement. Here's what I do, YMMV: to learn where to put my mics on my cabs, I have someone come over and play, and I put on headphones, and move the mic stand around - up, down, closer in, farther out, at various places on the speaker, etc. If all you do is stick the mic on the speaker and not try different mic placements, well...lazybones! Take notes! Take pictures with your iPhone! Put a little sticker on the speaker grille. Get out a tape measure and get the details down so you can reproduce what you're doing. Hell yes an inch makes a difference! Whatever you have to do to remember stuff.
When I record an acoustic instrument, I do the same thing. This is not rocket science, it's art. It's experimentation. It's personal preference. If you don't experiment a little, you're missing the point.
OK, all that established, we can move to mics.
For many years, my favorite mic to record an amp has been the SM57. It's the classic amp recording mic, it's inexpensive, it sounds good, and it's been a staple on hit after hit after hit for a very long time. I always laugh when people say, "I want my amp to sound live like the such-and-such recording of X hit." Yeah...well, you're hearing that record with the sound of the mic, the room, the processing, the tape, the console, the mastering, and the whole nine yards. But if you're recording, and you want that classic sound that sits really well in a track, the 57 is like putting a classic EQ on your amp, and it's an awfully good way to get there. I still use a 57 for certain things. It's especially good with high gain stuff.
Not too different from the 57 is an Audix i5. The i5 is a little fuller sounding and less nasal than a 57. Not a bad choice for gainy or clean amps.
This is becoming a classic: The Royer R-121 is a phenomenal ribbon mic. It's relatively sturdy for a ribbon, can handle amplifier sound pressure levels well, and sounds rich and warm. If you want a "big" sound, with some room in it (the mic is a figure-8 pattern mic, and "hears" from both front and back), and a warm top end (that is, the mic is a little dark which reduces fizz and spittiness from the amp), this is a fantastic choice, and is becoming my favorite mic for other uses as well. The Royer is expensive, but it's beautifully made, sounds great on bass, overheads, horns, female vocals, acoustic guitar, and piano, and is heads and shoulders ahead of older ribbons or the cheap stuff that comes from China. The AEA R-84 is super as well, but I don't own one. The ability to pick up sound from the rear means the mic is going to hear room even if it's placed close to the speaker, so it tends to sound very natural. For those of you who say, "How come the recording sounds nothing like what I hear in the room?" here's a good choice. Placement is critical. Reading the manual is critical - ribbons are fragile. A puff of wind can blow the ribbon out.
Blend the Royer with a 57 and you get a completely different thing...fullness plus a bit of raunch. Can be great. I actually prefer one OR t'other, but it's your call.
Finally, especially with a clean amp: You'd be surprised how fantastically accurate a Blue Dragonfly sounds miking an amp. It tends to be a little bright, so I'm less crazy about a condenser with overdrive, but man, clean it rocks. Also that moveable head is convenient for quick adjustments for placing it. The D-fly also sounds great with acoustic guitar and vocals. You can buy less expensive condensers for these purposes, but this is a very good general purpose mic, especially for the dollars. I prefer Blue's mouse for vocals, as its a little less diffuse-sounding, but the two are actually pretty close. However the Mouse doesn't kill me on amps.
So there you have it. These are my favorites for amp miking. I'm sure you have yours, and I'd like to hear about 'em!