I once compiled a short book list on medieval Russia for anglophone readers in: Books on medieval Russia.

The following are excerpt from the book list:

• Ostrowski, Donald & Christian Raffensperger (eds.). Portraits of Medieval Eastern Europe, 900–1400. London - New York: Routledge, 2017. (linked to the table of the content of the official site of the publisher)
• Ostrowski, Donald & Marshall T. Poe (eds.). Portraits of Old Russia: Imagined Lives of Ordinary People, 1300-1745. London-New York: Routledge, 2015 (linked to the official site of the publisher): There two book are actually not history books themselves, but, so to speak, collections of the 'imagined biographies' of some historical figures in medieval and early modern Russia (and Eastern Europe), written by the specialists and based on the researches. Thus, they serve as introductory books of this field of research. Ostrowski is also currently one of almost the only remaining figures in pre-modern Russian history in Anglophone historiography.

I suppose these two books (especially the first one) are written for non-experts and will serve as introductory works for this area and period. Each chapter also has some recommended literature on the person featured.

As for the Cumans, you can also refer to the following basic textbook on Central Europe since it touches a bit (only a little, though) on the relationship between Hungary and the Cumans:

• Nora Berend,Przemysław Urbańczyk & Przemysław Wiszewski, Central Europe in the High Middle Ages: Bohemia, Hungary and Poland, c.900–c.1300. Cambridge: Cambridge UP, 2013.

It is also difficult for me to find any not so strictly academic literature on medieval steppe people like the Bulgars and the Cumans in English. Florin Curta is a specialist in the Balkan Peninsula and the Slavs in the Early Middle Ages, so I hope that his textbook also covers the topic you're interested in (i.e. the Bulgars) enough:

• Curta, Florin, Southeastern Europe in the Middle Ages, 500-1250, Cambridge: Cambridge UP, 2006.