I find it difficult to play and sing separately with the same musical vibe. I used to multitrack friend's vocals and playing separately back in my 80's cassette 4-track days, but as I've progressed as an amateur musician, I find my self understanding why they would often complain about it not feeling natural or capturing the emotion of playing and singing like they normally would.
If you are only using two mics (or one stereo mic) to record and are not overdubbing, you're probably better off treating it like a 'live recording on stage' situation and mic'ing (X/Y, blumlien, whatever works best depending on your room, tone, sound balance) in front of the player (you) as discussed and trying to get a good balance of guitar & vocal. It can be simple, effective and very natural sounding (maybe too much so if you need embelishment)
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I do this at home for the same type stuff playing my Taylor 514, which is not so very loud, but is still more powerful than my weak untrained voice. I use my low-profile live mobile gear (4060>MMA6k>R-09) and tape the mics to either side of a 7" dense foam ball hung from the ceiling about midway between head and guitar. The foam ball acts as a head sized spherical baffle and works really well for a quick no-nonsense set up for one to several acoustic players in a tight circle. Nice sound stage as the back half of the circle flips over to the front on playback. Alone, you can get in close for a bigger, fuller sound that eliminates more room. Placement in the room and the room itself are important of course. Experiment and move around.
The 'vertical X/Y' you mention works best with the mic's set to fig-8 and the null points pointed at the sound hole of the guitar and the singers mouth, respectively. More like a 'vertical Blumlein' actually. The whole point of doing this is to try to get as much isolation between vocals and guitar as possible so that you can treat each differently with compression, reverb, etc. In that way it's more of a multi-tracking type technique. Of course the best isolation without compormising mic placement is laying down separate instrumental and vocal tracks like Chris & Ryan mention.
My gear selection is currently limited, but after I find a computer interface, I plan on using the same setup as above as a main pair and adding close mics to reinforce and massage the vocal and/or guitar separately as needed. The 'vertical Blumlein' would then be a good potential choice given it's isolation. Perhaps a more typical card on voice and another on guitar (or guitar direct) would work too. It may not work like I imagine, but my goal is more capturing a 'live' event happening between a couple players than assembling a tune piece by piece. Even if you end up tracking the guitar and vox separatley, you may find it hard to adapt to playing and/or singing while listening through headphones. It's a bit of a learned skill. Good closed 'phones are essential in setting up and positioning you and your gear when you are playing both engineer and talent, but if it hinders your performance, get it sounding right, then ditch the phones and nail one. You're the only one so it's not like you wont be able to hear over the drummer or something. Put on your engineers hat and get everything set, then relax, forget about the technical stuff and catch the magic and emotion.
That's what i've been thinking anyhow, but my quirky ways & opinions don't work for everyone. Let me know what ends up working best for you.