I just finished Bleak House which was the first Dickens I've ever read and I'm not sure I would recommend it to be someone else's first.
He's wonderful and by the end of the book I was fully engrossed but it took me a while to get there.
I had no idea what was going on for the first quarter of the book, since it had a fair bit of legal jargon, and stopping to look it up kept interrupting the story for me.
His style of writing (long, convoluted sentences, huge cast of characters) also confused me until I got used to it.
I haven't read any of his other works yet, but I feel like if I read something like Oliver Twist, where I know the basic story already, it would have been a gentler introduction to his style, since I would at least have a vague idea of what was going on from the beginning.
I might just be dense, of course, YMMV, but my suggestion is to try one of his very well known books first.
I'm probably going to read Bleak House again, because I think the whole thing will make more sense the second time around. I really did love it, but I almost gave up before I got to that point.