Wow, I can't believe I've never read through this whole thread. That's probably because the OP has already gotten such varied and good advice. The advice is varied because there are multiple ways to skin this proverbial cat. Pays your money and takes your choice:
1. You lazy bum! Just learn to play and sing the parts separately. No bleed, no problem.
2. The bleed is your friend. Avoid phase distortion by mic placement, and learn to love the bleed. Don't try fancy post-production tricks on the two tracks. Just let them be what they are.
3. Nonsense! We can defeat the bleed with better focus. Two figure 8's are usually used for this and can come very close to isolating the two tracks. A small baffle disc the size of a pop filter just below the player's chin will significantly improve the isolation. It will also annoy the guitarist no end.
4. Real men don't need no stinkin' stereo! Just get one good omni and find out where the sweet spot is. Use the California system. Move it around until the feeling is right.
5. (my least favorite) We'll fix it in the mix! We'll EQ that damned guitar until you don't even recognize it!
I have seen every one of these systems used, and personally survived most of them. I prefer #1 in most cases. If that isn't possible... here's my #5: It's the stereo version of #4- I often use a more distant, one point stereo image, either mid-side or coincedent, and find the sweet spot in the room. You need a good room for this. If the room is not so good, the mic array is moved closer, up to a point. I will record from 4'-6' distance, usually. I then build the mix from the stereo guide track. I do the MS thing with several different combos. B.L.U.E. Kiwi (fig8 or cardioid)/AKG C414 (fig8 or cardioid), C414 or Kiwi in fugure8 with Rode NTK/Neumann KM184/AKG C2000B as the cardioid. For a coincedent (X-Y) pair, I have to use small diaphragms, because (damn), I don't have a pair of LD condensers! I find the Neumann's cruel, unless you have a hell of a singer-songwriter in the house. What the hell? The beatles used KM84's that way. I used to use Oktava MC012 as a stereo pair, but C2000B just kind of took over that role.They're pretty cheap, as they go, and make a great stereo pair for guitar/vocals. Best of luck.-Richie