The mic you use depends on your budget. A dynamic mic (eg the SM57/58) do good jobs at the lower end of the price scale. Condenser mics however capture a wider range of frequencies during recording so therefore sound slightly better, although this is based on the preference of the player. They are more expensive however, with some going up to and beyond £1500. For a good, cheaper condenser mic that still does a good job I would recommend the Rode NT5.
When it comes to recording, position the mic about 30-40cm away from the guitar, at about the level with of the lower end of the fretboard (near the sound hole). Angle the microphone body towards the sound hole from it's position. You can experiment with what gets the sound that you want, moving the mic around. Trying different mic techniques can also be interesting. I have known people to place one mic pointing at the fretboard, and one down at the sound hole, to give an interesting stereo effect.
And yes, plugging the output cable from an electro-acoustic into an audio interface is absolutely fine. From there, inside the software, you can change the EQ, put effects and reverb and whatnot on the recording.
Note however that the output from an electro-acoustic sounds different from a mic-recorded acoustic guitar. Sometimes you just want that background strumming (particularly with twelve-strings) sound that electro-acoustics don't always produce.
Hope this helps :)