Overview:
Build: Impressively, though naturally, lanky. Long lean muscle, but not much of it, because I imagine him to have the kind of body type where not eating enough and moving enough consistently means the muscle just keeps sliding off. Not girly sort of frail, just bony and long-limbed. Pretty bendy, very fast, but not enough muscle to have much endurance. Sharp shoulders, very narrow waist, quite narrow hips too.
So mostly as in the current age comic canon, really.
Personality: we're looking at someone quite erratic. Similar to schizophrenia, but also with a mentality that's given up on the societal norms entirely. Societies crumble and leave people raving monsters, so nothing he does is going to change that. Of course, add in some severe bipolar and a lot of unexpected triggers. He's not 'crazy' so much as 'painfully unstable', I guess. I mean, he IS crazy, but that's not what defines the way he acts.
Background: Chemically induced brain damage and some pretty thoroughly repressed memories stop it from being something he knows. Maybe Batman could work it out, if he really tried, but it's not really the main issue, so Bats ignores it, I guess. It'd take a lot of effort better used in making people less killed.
Specifics:
Skin - not albino-pale, where it's translucent, but the pigmentation, the melatonin in his skin, is actually WHITE. So obviously it can still blemish and bruise, and he can blush, and where the skin vessels are so close that they change a dark-skinned man's skin tone - nipples, genitals, lips, around the eyes, in the nose, etc - you can see some colour. Which also means that it can be sort of patchy-ish, if there's something wrong with his skin somewhere, and since he eats reeeaally badly when he's broken out, malnutrition has left faintly grey patches on his skin. Also, there's some roughness from scars and burns that leave super obvious marks on his white skin.
Hair: Green, but not totally solid single tone. It's a 'natural' green, so like a natural brown or natural blond, there's various shades in there. In some spots, there's almost a brown tinge, and as he 'greys', it's going wintergreen at his temples.
Facial structure: Narrow and bony, but not a caricature. Long-faced to a believable extent, wide mouth, long sharp nose with a narrow bridge. No giant chin, no impossible/improbable nose.
Eyes: Probably naturally rather vivid green, for preference, though a pigment-free red might work, with small pupils from the high adrenalin, and makeup, yeah. He doesn't like the veins crisscrossing his eyelids from lack of sleep and so on, and the pinkness, so sometimes he wears eye makeup, sometimes not. Depends on the mood.
Mouth: Doesn't need lipstick, his lips are so close to pure red, so delicately free of pigment - from being damaged by the chemicals, so they're thin-skinned and prone to split easily - that holding a red swatch next to them, there's no difference visible. Free movement, though rather broad outwards, and slightly thin.
Smile: The smile itself, not a frozen one or a chelsea smile or anything. He grins automatically when he's feeling awkward, or cheerful, or nervous, or angry, or most emotions. And he's pretty hyperactive, so he finds a lot fun.
Clothes: BIG WARDROBE. Like, super huge. He likes purple suits and coats, because they flare out against his skin and hair and look so vibrant, but he likes to impress. Sometimes he'll go for a suit, sometimes he'll go for something shabby. Depends on mood, really. No totally automatic costume to wear. He's trying to accentuate the 'clown' aspect while still being snappy enough to intimidate and cause people to double-take.
Themes: Would be - mocking. Sometimes grimly, sometimes cheerfully. How bleak the humour was would have nothing to do with how terrible the crime was. World-weary cutting sarcasm humour Joker stealing a few hams for the hyenas, giggly childish, bright-eyed Joker gassing thirty Arkham staff members - either works. Sleight of hand and other things which involve hand dexterity, too.
Acting/Effects:
Voice: Close to Heath's, but without the twang to it. Think of Heath's voice, with Mark Hamill's inflections and nuances, and then add in Cesare Ramero's absolute delighted little sound, and Heath's growl but Hamill's various laughs. A bit more expressive than Heath's voice, which was ominous; I reeeallly liked that depiction and had a pathetic man-crush on him for a while because of it, but Joker's most jarring when he's bizarre. (I think that's why the Nolanverse works so well; it seems so close to real, which makes our 'heroes' and our 'villains' both seem utterly warped. I like it, though Joker seemed less crazy, to me, than Crane in the preceding movie.)
Makeup effects?:
Perhaps an albino actor with powder. Eyeliner and shadow on the eyes, but not too panda-esque. Red lips, probably with pencil rather than lipstick, so they look naturally coloured and not glossy.