Cant really think of any combination of stats they would specifically want. AD assassins differ from ADC in that they want AD, Armor Penetration and Movement Speed While ADC want AD, attack speed and Crit chance. Meanwhile it Seems that all spell reliant AP champions just want AP, CDR and Mana,
AP assassins generally don't want mana, just because any item containing it is going to either a) take too long to build up or b) gonna have crappier other stats.
So it is less AP assassins building differently from other AP champs and more other AP champs building differently from them.
AP Assassin want Movement speed/mobility, AP, and MR Pen and if CDR.
The required stats are all relative to the champion. Champions like fizz and diana are extremely upfront with no safety to their kits so they tend to want to build on the tankier side. Fizz prioritizes defensive stats and CDR because he's extremely vulnerable to getting locked down and killed or just outright counter bursted. Diana tends to build RoA first item with maybe 1 defensive item (Hourglass or Abyssal) then straight AP as her RoA and shield work great for making her tanky.
Meanwhile, champions like Leblanc doesn't need any of this as she's 100 times safer. Thus, the only stats she really needs is CDR and raw damage.
Cheap early combat stats like ap, mr, ar, hp, mpen and damage/defense passive/actives. Mana is usually a waste of gold and cdr is overrated on assassins in my opinion.
Magic Pen, AP, and Movement Speed.
ap assassins don't want more stats, they want onspell abilities that scale
or if you mean in general they want whatever kills the target lol. But you have ot consider things
if you can kill them in one rotation you want
if you have to dive a lot you might want or 
or both
if you gotta deal with a good defender go
