What's your go-to mic for recording guitar amp?

I usually use 2 mics. An SM57 or MD421 up next to the grill cloth pointed at where the dust cap meets the cone. Across from that one, on the other side of the speaker, I will use either my old AKG D12E or Royer R121 ribbon placed about half way between the dust cap and the surround. Make sure the distance from the speaker and capsules in the mic are the same otherwise there can and will be phase issues. If there is a wind screen built into the mic it is sometimes hard to see the capsule or ribbon. If you're not sure, set the mics and record a pass with each mic on its own designated track. Then zoom in on the wave forms and see if they line up with each other. If not, move one of the mics a little and record another pass. Keep doing that until the phase aligns.  Once phase alignment is correct you can scrutinize the sound coming from the amp and make adjustments to the controls.

You can also use a large diaphragm condenser (LDC) mic.  Usually with a cardioid pattern but make sure it's sound pressure level is rated high enough it won't damage the mic. Most modern LDC's will handle those levels but you need to make sure. If the mic has a built in pad you will likely need to engage it. When using an LDC I don't usually put it as close to the speaker. Since only one mic is being used it needs to be back a foot or more in order for the sounds coming off the different parts of the speaker to have enough distance to converge. I will place it off axis a little to minimize the screech coming off the center of the speaker.  Keep in mind that using a cardioid pattern will also give you some bass-boost due to the proximity effect of the pattern.  It can be an advantage or disadvantage.  Just remain aware of it and use distance from the source as an additional tone adjustment.  That is true of dynamic mics as well.

Smaller combo guitar amps usually sound better when they are up off the floor a foot or so. If the mics are close to the floor there can be reflections that can interfere with the mics. When miking up a 4-12's cabinet I always mic one of the top speakers so the floor reflections aren't as much of an issue. They can also sound better/worse placed in different locations in the room.  I don't like having the amps close to a wall.  Out in the room usually sounds better to me.

That's how I do it. There are those who also mic the back of the speaker in an open-back cabinet. The sound coming from the rear of the speaker is quite different so that can be blended in with the front mics for an additional tone source. The polarity on the rear mic will have to be reversed and the phase with the mic placement will also need aligning via distance from the speaker. I have never found the need to mic the rear but many people do.

I have used ambient room mics before but haven't done that in a long time. The room needs to sound half decent and if it's a small room the sound can be, and is often, unpleasant. If you want to use an ambient mic and your room is less than stellar try putting one down the hallway outside the room. Opening and closing doors to other rooms that access the hallway can change the sound of the ambient mic. Sometimes for the better sometimes not.

Experimentation is key with any recording setups that involve microphones. I like to do my experimenting on days I am not working on a project. That way it doesn't interfere with the creative flow of the musical development. Technical issues are Kryptonite to me when I'm recording and wearing all the hats. I hate them when trying to record something by myself. On an experimentation day I can throw a number of different mics at something, different placements, different mic preamp combinations, different amps/locations, different guitars, etc. I always try to document what I learn on those days so I can come back to it. Guitar(s) used, amps used, amp location in the room, room dimensions/treatment, GOBOS or not, mic settings, preamp settings. Anything that is pertinent to what controls the sound. A tape measure is your friend.

e906's are nice mics and many people use them as amp mics.  I don't have one and have never used one so I can't offer any help with that.  I don't see why you shouldn't be able to achieve great results using it.  Throw up the SM57 too.  That way you can get an idea of any tonal differences between the different mics.  Make notes as to the differences you hear.  There may be a time in the future you may need the more pronounced effect of one mic over the other.

I can talk about this stuff all day.

I don't really like 57s, so I use condensers typically.

My go-to are the old Oktava pencil mics pretty damn close to the grill, and a couple large diaphragm condensers in the room to capture air (I have 1200 sqft in my recording area)

I'm not a fan of the SM57 sound on cabs, and found the Oktavas did it for me when I don't have a ribbon

Taking detailed notes and filing them away is a great way to learn about mic placement and recording setups. I have a notebook with lots of this kind of detailed information in it. I hardly ever look at it anymore but I used to reference it often.

It's also a good idea to include the room size, notes on room acoustics and treatment, and speaker cab placement in the room. A tape measure is a good way to document that. Make a small sketch of the placement in the room as if you were looking down at it from above and note the appropriate dimensions. It doesn't have to be exact. Within 6" to a foot is close enough. Next time you record try putting the amp in a little different place in the room and see if it sounds any better or different. Close miking helps eliminate the room some but it can still have a bearing on the sound.