For PIE, the most accessible recent book in English is probably
The Horse, the Wheel, and Language (Anthony 2007), and I would highly recommend it. (It pulls double duty as a laymen's
and as an academic publication, so if you do read it, know that it's OK to skip the minutiae of pottery shards.)
A slightly older but enduringly popular work is In Search of the Indo-Europeans: Language, Archaeology, and Myth (Mallory 1989). I'm told How to Kill a Dragon: Aspects of Indo-European Poetics (Watkins 1995) is very good too, but I have not read it myself.
Chapter 2 of Indo-European Language and Culture: An Introduction (Fortson 2004) is a very good summary of PIE culture. The book is excellent in general - probably the best English language introduction to PIE linguistics at the moment - but outside the first two chapters it is not generally accessible to laymen.
If you read other European languages it's worth checking out other books that may be available to you. The field by definition requires the ability to read a decent number of languages, so the literature is spread out across English, German, French, Russian, etc.
