Another voice added to the "this book ain't necessarily easy" chorus.
If you want a collection of "VERY simple pieces", suitable for a beginner, I'd recommend the Palmer-Hughes Recital Books, if you can find them across the pond. Either Book 2 (early beginner) or Book 3 (intermediate beginner). They're very well-edited, with excellent notation, fingerings, etc.
If you're okay with the lead sheet format, you could give Dave Mallinson's "Easy Peasy Tunes" a shot. No fingerings there though (it's not specific to any particular instrument).