Well, it's been almost ten years since I read Russel, and while I liked him at the time, I've done a lot of primary-source reading and I now agree that any reputation he might have for bias is very well deserved. Russell is absolutely a creature of the Western analytic tradition, seems almost incapable of taking anything else seriously, and engages in ad hominem (e.g, his section on Nietzsche) when he doesn't have anything to offer.

Reading Russell can easily give you a mistaken view of the thoughts of other philosophers, especially the more they diverge from Russell's opinions, which are by no means the indisputably correct ones.

Really, I think the OP should avoid reading the history of philosophy specifically, and focus just on general history. I'd recommend reading the classics, and always try to find the most complete works that are the most contemporary - read Herodotus, read Thucydides, read Tacitus, read Caesar, read Plutarch, read Carlyle, etc. You get a hugely different experience reading how people at the time thought and acted from their own perspective, or as close as you can get to it - at least from the perspective of someone who isn't a 20th or 21st century American with the associated values.