We need much more information to make the best recommendation for optics on your new rifle.
Let's make it simpler, Sell it to my wife (cheap) and she can give it to me for Christmas or my birthday. That way optics will be MY problem, saving you all this anguish & saving my wife from figuring what might be "the right" gift!
If that doesn't work, & you still want to put optics on it, consider Nightforce the bottom-end for your search. Anyone using a .338 Edge means to reach WAY out & touch something, & you can only hit what you can see, so quality optics are mandatory. I would think a 5-20x50mm class scope would be the minimum for a .338 Edge. Knowing how your rifle will be used will define things from there. If you go above 20x & want to see under poor light bump up to a 56mm objective lens. The offset on your rail will depend on what scope you choose & what adjustment range it has.
I really like the Horus reticle that Nightforce is offering on the NXS scopes. It's alien to some since it's not what they grew up with, but for me it is simplicity personified. If I were to be given such a rifle, I know that's what I would put on it.
Wish I could offer more specifics but you didn't give us much info to go on.