I also am on the look out for A History of Western Philosophy by Bertrand Russell. I know from a previous encounter that his style is very readable for me.
I'm a great admirer of Russell's work, and I think his style of his writing is second only to Hume in the English language, but I must really dis-recommend this particular book for a few reasons. Off the bat, it spends far too much time on Ancient Philosophy for an introductory text to Western Philosophy as a whole. The time it does spend on modern philosophy is often simplistic and problematically selective; Russell is outright dismissive of philosophers of which he has no personal interest. And most damningly in my view, the book shows a complete poverty of understanding of Kantian metaphysics, and of idealism and transcendental idealism in general.
If I could recommend one "general" book on philosophy, I'd instead recommend
Confessions of a Philosopher by Bryan Magee. It's not really a proper autobiography, but rather a story about the history of philosophy as told through the eyes of a modern philosopher. This leaves some things out, of course, but I find that the virtues of this personal approach to philosophy (the only way to approach philosophy, I think) outweigh the obvious disadvantages.
Magee has written another book of a more conventional style titled
The Great Philosophers: An Introduction to Western Philosophy. I haven't read it myself, although from my experience with Magee's other works I am very confident it'd be much more fruitful and insightful to you than Russell's
History.