Welcome,
Not trying to be rude(especially on your first post),but...
You have a sporter weight .338-378 and you are worried about recoil due to the weight of the bullet?! Before you purchased the rifle did you ever shoot your dad's .30? If so I'm sure the .338 is gonna be worse.
I don't have any experience with elk (and the way things are going may never!) but from your post it sounds like you don't have much long range experience so I'm guessing your ranges aren't gonna be what most on here would be considered looooong. So in saying that, and due to the size of your new cannon, I would tell you to shoot a premium well constructed bullet of at least 225gr.
As far as the scope goes, I'm the last person that should give advise on what scope to buy. I will however give you some advise on what not to buy. I highly recommend against the purchase of a 3-18 IOR (FFP or SFP) for THAT rifle. My 15+lb Edge doesn't have near the recoil your sporter .338-378 will and I broke three (2 FFP and 1 SFP) on the Edge. They just wouldn't hold up.
If you are considering a Leupold the VH reticle is great in bright light on light or bright colored targets but likes to hide on me against dark(black) targets and in low light. Not much use for your average hunting conditions.
Just my observations...