If you are strictly looking for a standalone digital recorder, I'd suggest maybe pushing the budget to the level of something that has a couple XLR inputs, so you have the option of plugging in a couple separate mics as well, to give you some balance between voice and guitar that is hard to achieve with a single mic, or a small XY configuration that these units have.
I'm a Zoom fan - still have the original H2, and used an H6 for years. Now I've got an F8 and F8n. The Zoom H4n Pro is the lowest Zoom model with XLR inputs. There are other manufacturers, of course, so check reviews, etc.
Get a boom mic stand with an adapter (or two!) that will allow you a lot of flexibility in how you position the recorder so you can get the best results.
There are lots of other ways to do this, of course, many already suggested. To some degree it depends on what you want to do with the recording, i.e., what kind of end result are you hoping to achieve, what will you do with the recordings once completed, and how technically involved you want to get in that process.
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"I know in the morning that it's gonna be good, when I stick out my elbows and they don't bump wood." - Bill Kirchen
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