If you could add one or more new stats to the game, what would it be? (My first inclination is Luck, Accuracy and Evasion stats)

Well, I’ve talked about accuracy and evasion before here, and luck here, and my general inclination is that I don’t like any of them; I think the game is actually probably worse, not better, if you make those things into trainable stats.  I’m honestly not sure I would change anything unless I were rebuilding the entire battle system to function in a different way – like, I’ve vaguely toyed with the idea of having more of a 2D tactics-oriented system on an isometric or hexagonal grid, sort of like what Conquest has, and in that case you might, for instance, want separate stats for movement speed and initiative (for determining turn order).  Or you might ditch the idea of separate defence and special defence stats, and instead split HP into toughness and will, where low or zero will doesn’t actually knock a Pokémon out but does impose steadily worsening penalties.  There’s a lot of different things you could do that might be interesting, but I don’t think any of them would necessarily involve just slapping on an extra stat without reshuffling a bunch of other things; the basic system is pretty solid, I think.