That is a pretty straight forward acoustic sound. As with any recording you should start with the best instrument/musician you can afford (unless you're going for special sounds) so you're right with the decent guitar.
It sounds like (to me) that this recording used a piezo pickup rather than miking or using a magnetic pickup. What method you use to record acoustic guitar depends on many factors: how loud is the stage volume? does the artist need to move around a lot? what style of music will be played?
I'm guessing that the monitors were screaming hence they used a piezo pickup to help avoid feedback. Your humbucker will have more low end response than a piezo pickup, so if you choose to record with it you will have to roll off more lows (low shelf -3 to -6 from 500Hz down, again guessing).
Different mics will all sound different and what's even more depressing is moving a mic even 1/2" makes a drastic change in sound picked up. A good place to start is placing a condenser mic about 3"-6" away from the end of the fretboard. This keeps it out of the way of the strumming hand and gets good output from the soundhole. For more fret noise/high end stuff angle the mic more towards the nut, for more bassy sounds turn the mic into the soundhole.
As far as EQ you're probably heading in the right direction but also remember that compression was probably used and it can do as much to affect sound as EQ. Distortion, however is never appropriate in acoustic music (normally).