I'm going to be the lone naysayer here, and recommend against Russell's book.
Russell is an eloquent, entertaining, and engaging writer. I used to be a huge Russell fan myself when I was young, and back then I would have recommended his book too.
But then I actually studied philosophy and realized how myopic, limited, and biased Russell was outside his areas of specialty (Analytic philosophy, math, and logic).
Yes, you'd get an overview of (some of) Western philosophy from his book, but it'd be really biased, and that's the wrong foot to start you learning of philosophy from.
Much better, in my view, to just start reading the Socratic dialogues yourself, as part of an intro to philosophy class, instead of being fed regurgitated, abridged, predigested knowledge by someone with an agenda.
My view on Russell extends to many of the other recommendations elsewhere in this thread of books by other authors who've written overviews of philosophy from an Analytic perspective. They might have more up-to-date views than Russell did (who was born in 1872 and wrote his book in 1946), but they tend to share his limitations.