Ffenestri (Windows), by Lois Arnold, herself a Welsh learner and now an author, is a wonderful collection of stories and poems aimed at adult learners. Arnold cleverly divides the book into graded sections aimed at different levels of learner from mynediad (entry level) to canolradd (intermediate). Each section contains stories and poems on a variety of themes, meaning there's something for everyone here.
There's a real satisfaction the first time you finish reading a piece in a new language, and Lois Arnold makes it easy to be satisfied as everyone should find at least something that's within their ability. The stories and poems start using only the present tense, making them accessible even to those who are quite new to Welsh, and the reader is aided by a glossary of new terms at the bottom of every page. The difficulty level then gradually increases as new words and tenses are introduced. The stories and poems cover myriad subjects from cases of mistaken identity, to muddy festivals, space exploration and quiz nights. And they're not just filler material; each story and poem is a good piece in its own right.
I got great enjoyment from Ffenestri and it's a book I would recommend to anyone just starting out in Welsh. The short nature of the pieces means you don't get bogged down in a long story, and if you happen to pick something a little too difficult you're not stuck with it for the long run. The glossary means you're not constantly referring to a dictionary and thus interrupting your flow and enjoyment of the material.