The best overall biography of Timur is The Rise and Rule of Tamerlane by Beatrice Forbes Manz. Chinggis/Genghis Khan is a bit of a unique case because there's exactly one primary narrative source from an unmediated Mongol perspective, so I'd basically just recommend you read that: The Secret History of the Mongols, widely available in translation. I'm afraid I can't help with Attila (I would guess the sources for him are thin) or Kublai Khan (not really a steppe warlord).

One more person I'd like to sneak in to this list, although he was only ever semi-nomadic and not from the steppes: Babur, the first Mughal Emperor. I mention him because he's coming out of that nomad conquerer tradition, but also just because he left us a really wonderful, engaging autobiography. He comes off very human and flawed and likable, which is not the norm in my experience for premodern autobiographers! You can buy a nice paperback of the Baburnama in translation on Amazon.

Genghis Khan and the Making of the Modern World by Jack Weatherford is a good book to learn about Genghis Khan and his successors. it also covers the Toluid Civil War and the reign of Kublai Khan. There are also several translations of the Secret History of the Mongols available online for downloading. The link to the one I read can be found here.

There's actually not alot of selection out there. Academics have tended to focus on specific themes surrounding the Mongols, Timurids and other Steppe armies, or more gnera histories such as David Morgan's The Mongols or George Lane's recent A Short History of the Mongols. Because definitive facts about each ruler are few and far between due to a paucity of reliable first hand accounts, popular history writers have been able to write biographies that take in most of the known facts, even if the writing and storytelling can be variable.

John Man has written biographies of all of the above leaders, and they're not bad. John spends alot of time in Mongolia, which has given him an insight into the land that not all the historians have, but he is an adventurer and populariser rather than an academic historian (sorry, don't mean to sound snooty there!). I would definitely recommend his books to get a good overall narrative of each of their lives.

For Chinggis (Genghis) Khan, I would also recommend Frank McLynn's biography of him, which I think is exceptionally well written and entertaining, as well as historically correct.