Statikk Shiv has problems similar with the old Ionian Spark, except that it procs even less. It was obviously intended for clearing minions faster, but I feel Hurricane and Tiamat do this far better. I have yet to see Statikk Shiv used with success -- it is a hybrid item focused on doing two sources of damage introduced in the season where penetrations have been reversed and it is much more effective to stack one type of damage/penetration.
Of course, I personally feel that no onhit build currently outshines a build that goes AD or AP, but perhaps someone will prove me wrong on that. I just don't think they will with how penetrations have been changed now.
In short, Shiv would simply have been stronger in Season 2.
For AD Ezreal you can either go for Cleaver or Iceborn right away. It depends on whether you want more poke, or if you have a team with more peel and can go deeper into the fray. I recommend getting both, though, it's just a matter of which to start with. Some Ezreals will also want to start Tear for Muramana, which I have also seen work.