I would go with an RE320 for that money and your situation, they do well in the small uncontrolled room and have a great sound. But then again the RE20/320 are probably my favorite mics so I am biased.

Edit: Regarding pattern, cardioid tends to be most versatile as an only mic for the bedroom musician in my experience, you can get them back far enough to do things like pick up voice and guitar at the same time without much issue while still being able to effectively use mic position to mix the two sources. And it is narrow enough that you can stick stick it up close to a source and not deal with unwanted pickup on those days you have a lot of ambient noise.

Edit2: Somewhat retract my comment on cardioid, I can make as good of a case for hyper/super cardioid and in some uses they could be better.