I think you are too hard on yourself — Your playing sounded great to me!
The sound quality of the Zoom H1 sounds pretty good. I've never actually heard a recording made with one before, but it's nice and clear.
I bought a Snowball mic, a while back, and I was looking at some of the Zoom range at the same time. The Snowball's great, but it's very sensitive, and picks up a lot of background noise, and also fan noise etc. from the PC, so I had to build a mini sound booth to clean it up.
After hearing your recording, I might go ahead and purchase a Zoom mic — but probably not the Zoom H6 at circa £300.00 ($400.00).