Ok. I just played Thresh in PBE Custom with BOTS (I know it's not the best place to test but whatevs). I tried two builds.
Firstly AP. All his moves are scaled AP except his Q Passive (If I can remember). His ult does a ton of damage if you set it up right (making the enemy hit two walls) and he doesn't really pull but rather drags the enemy at two intervals (also hits the first thing where it be a champion or minion). And you can use E while Q is dragging the enemy.
My 2nd try with AD/AS was much more effective IMO. His long range is able to hit an enemy when they are escaping and with your Q and E it makes it even harder for the enemy not to get hit by your AA. During late game, if farmed a lot 200 souls give approx 110 Bonus AP/Armor (can't remember how much armor you get) but I think about 50 - 70 souls, the AP gained is half (0.5) and will keep giving you half onwards. My build was Beserker Greaves, Zephyr, Infinity Edge, Trinity Force, Phantom Dancers and Hextech Gunblade. Probably the most impractical build but it gave me about 1.8-9Attack Speed, Lifesteal and Spellvamp, 65% Crit chance, approx 270 AD and AP (approx 110 AP from souls) and his movement speed was about 472 (included the 15+ MS bonus movement speed from boots). This build allowed me to chase and hit at a pretty safe distance as his AA is by far the longest i've seen for a melee champ.
Well this is my contribution. Probs not the best. xD