Ap Jax

I've never done it but I'll guess one for you....

or and a or a

Depends on your goals. Do you just wanna deal tons of magic damage? Do you care if you survive fights? (Are you only split pushing & dueling, otherwise running?) Are you looking to lay the smack down in teamfights with tons of magic damage?

I'd always get a BOTRK. It deals a bunch of extra magic damage and increases your attack speed which stacks your passive faster and stacks your ult's passive faster.

Wit's end is a reasonable choice as well; more synergy with BOTRK's attack speed, more magic damage on hit, and more attack speed to get botrk & ult passive & your passive stuff up faster.

After that it depends on what your goal is. You may build a nashor's tooth for even more on hit madness, will be excellent duelist, but kinda weak in teamfights.

So core is: boots, botrk, wit's end

Option 1: tons of damage, good duelist, shitty teamfight (too squishy). Great splitpusher. nashors, rabadon's, lichbane

Option 2: Pretty damn tanky, decent damage Randuins, Banshee's veil, warmog's

Option 3: reasonably tanky, good damage. triforce, bveil, randuins

BotRK doesnt deal magic damage, it deals physical damage, from both his passive and active effects: http://leagueoflegends.wikia.com/wiki/Blade_of_the_Ruined_King

, , and would be core i think. Beyond that, it's Jax; you can build anything you want and still carry

Edit: forgot about , that's a good one for AP Jax