Well I didn't record Nothing else matters, but can tell it's done on a classical guitar in front of a mic - no amp at all. You would want to just use a clean channel on your amp with your guitar to get closest to the sound, use your neck pickups, not the bridge (neck pickups sound deeper because the string vibrates more there). Neck pickup means the pickups closest to the fretboard. Use a low tone on your guitar (located below the volume knob on most guitars) and thicken your electric sound by adjusting your amp to boost the lower sounds. Also, remove the treble / presence a bit. Basically you want to eliminate that jangly sound you get from clean electric guitars. That jangle is great for country and folk music, but not this kind of classical style.
However, I did record enter sandman, and used a Digitech RP(250 I think?) through a Peavey 80W amp. I set it to have a lot of distortion with just a little bit of phaser in the sound. To get that on your amp, you'll need a lot of overdrive (fullest setting probably), just a touch of flanger (this will be very similar to a phaser effect), and add a tiny bit of delay (this will thicken your guitar sound). Also, I used humbucker pickups at the bridge position (the pickups closest to where the strings terminate - furthest from the fretboard). On most guitars this means flicking your pickup selector all the way down (and all the way up if you want the neck pickup for nothing else matters). I also put the tone fully up to 10...to get some 'edge' into the picking sound. Using the digitech pedal (like I did) helps get you different sounds, so don't be surprised if you can't get it sounding exactly the same! There's a big difference between our two amp setups there.
Hope that helps...and isnt' too confusing

PS....As for the thumb....it really just takes time and practice. My guitar teacher used to smack mine with a ruler every time it crept up like that

Don't worry, it's a common problem, with time you'll get it. It's not altogether bad either. It's useful for some guitar styles to use your thumb over the top edge of the fretboard (usually when strumming chords and muting out the lowest strings - like with D or A open chords). However, that stuff comes later...make sure you get comfy with the basics first. You need the thumb in the back to get proper strength into fretting notes. Later when your fingers are stronger and more used to playing you can relax the rules more.