"The New Tsar" is a good account of Putin's "Rise" and "Reign." Steven Lee Myers is a journalist and in many ways it shows throughout the text that what you're reading are almost extended journalistic pieces of famous events/personalities that made headlines in their time rather than in-depth historical coverage. Some of the topics covered in one or two chapters (Beslan, Kursk, Chechnia, Yukos affair, etc.) have entire volumes dedicated to them by historians and scholars that often do more justice to them than the space provided for here. Nonetheless, what Myers does well is congest a lot of information into a readable account, pretty much what journalists are paid to do. The majority of the text leans from unbiased to somewhat biased (against Russia/Putin), not that one can fault Myers, Putin and his time in office have witnessed numerous disasters, mysterious deaths, wars, the jailing of prominent members of Russian society, etc.
A more subjective approach, however, I think would have been helpful for western readers to gain a sense of where Putin and the many Russians who support him are coming from - even if their arguments are often laced with familiar propaganda. There is a lot to learn here for those somewhat familiar with the Russia of the post-Soviet period, those totally unfamiliar might get lost among the many names, places, and events that Myers goes over with, at times, the briefest of descriptions. Personally, I've long suspected that Putin's Russia is less so guided by ideology than by Geo-politics and economics, which often come into direct conflict with European and American organizations that appear to Russia as encroaching on her "spheres of influence."
Russia often appears to be the epitome of crony capitalism, the revolving door that we're so familiar with in the US (between corporations and political positions) is a given in Putin's administration, except it's more brazen than in the west. Embezzling, fraud, tax evasion, etc., are all prevalent within the Russian economy, but its fallout is usually much easier to spot than in the US where our economy and GDP dwarf Russia to enough of a degree that billions can be siphoned off and usually forgotten about within a matter of months if not weeks. It's as if Russia has taken the worst aspects of capitalism that exist in the US and around the world and applied them to the 10th degree. While some of Putin's early reforms helped raise the average Russian's economic situation in terms of buying power and savings, what has happened after that initial term in the early 2000s has been a policy of attempting to strengthen the state to the detriment of any and all "democratic" institutions that might have existed. This enriching of friends and focusing power within the hands of a "loyal entourage" means Putin becomes that much more frightened of what will happen once he's out of office. What he undid after Yeltsin stepped down is undoubtedly in the back of his mind and his losing power seems an impossibility in the near future as his popularity continues permeate much of the Russian population.