I think every artistic depiction I've seen is of Jaime in his evil glory, whereas in the books, he has much more screen time as one-handed, changed Jaime.

I think that's because a lot of the illustrations are for those games so it's not about what happened in the books. Or something. But the Jaime *I* love so much is the one we first get to know in the dungeons of Riverrun and I'd imagine he's looking a bit shopworn by then :P (And *then* he loses his hand!!)