My Reasoning on Ability Order

     Catwoman, like most blasters in bot lane, tends to initally have slow wave clear in early levels.  With the beginning level 3 start that you are given on GH, i usually go with two levels in her Q and one in her E.  This allows you to have a better chance within the first couple of levels to fully destroy the minion wave or at least damage it to a level to where you can basic attack to finish them off. 

     Then put one point into her W, before maxing her passive, taking her R when available.  I usually max her passive due to the extra credit gain and cdr reduction for all of her skills.  Some matchups in bot lane will require you to forego maxing the passive due to damage output against certain champions or defensive presence of others .

    Once passive is maxed, i follow by maxing Q, E, then finally W.  The reason i max W last is because at level 1 i generally use it for the E-W knockdown followed by Q for safe harassment.  Q is maxed second for the E-Q combo for team fights due to the AOE damage. E is maxed third for the bonus damage to Q and increased knockdown time for W.