My understanding of it is that the English, Irish, Canadian BCPs are one "stream" based on the 1552 Prayer Book as mostly adopted in 1559 and 1662. This includes a more distinctly Reformed Communion service than the Scottish/American Prayer Books that are based on the 1549, which is more Lutheran in orientation. The 1552 came out of reforms and changes suggested by Vermigli and Bucer.
For daily use, Morning Prayer and Evening Prayer in the 1662 are pretty unobjectionable. If you don't want to use the optional hymn partially based on the apocrypha (Benedicite, omnia opera), it's based on Psalm 148, so I just use that (and could even use it exclusively if you only wish to sing inspired texts).
The thing that's tricky about the BCP is that in many ways it IS the "larger catechism" of the Anglican church in that the doctrine is baked into the set liturgy for a given situation (marriage, baptism, burial, etc...) rather than separated off into questions and answers. To the extent it's solidly Reformed, which the 1662 definitely is in many parts, it's fantastic, with some areas being especially superb (Trinitarian prayers and how to pray rich and meaningful short prayers more generally). The extent and breadth of the scripture readings in Morning and Evening prayers, especially the Psalms, provide a real challenge.
To the extent it's either Lutheran or Anglo-Catholic, depending on the version (newer is worse for the most part), those compromises really creep up. What a lot of the "trendy" Anglicans neither realize nor care about if they do is that one of the biggest Puritan objections to the BCP, especially the 1662, is that all of those feasts and fasts beyond even the "normal" "holy days" like Christmas, Easter, Pentecost, and the like are mandatory and confessional, and there's a LOT of them. It's a pretty heavy yoke in my opinion. 4 centuries removed from the conflicts and in an age where even a little conformity would be an improvement over most of what passes for Anglicanism, the issues are different.
But Morning and Evening Prayer are quite good and worthwhile to chew on, especially if devotional time is a little stale, as well as some of the prayers within other sections of the book.