If you are going on a guided hunt any flat shooting cartridge that will kill deer will kill caribou. The only reason to carry the .338 would be bear protection if one wanted to take your caribou from you (but the guide should keep bears from killing you). I've been using Vortex optics and have had very good luck with them. The Weatherby Mark V Lighweight rifles are good ones.
budsgunshop.com/catalog/product_info.php/products_id/4316/Weatherby+Mark+V+UL+Bolt+300WBY+Mag+28in+3%2B1 />

If you feel my answer is helpful please click the green box stating it as
the best answer. We are rated on our answers and are just volunteers.
Thank you!

I would decide on what Rifle I wanted and take either of the two calibers ( 338 vs 300 win mag) that it was available in the Rifle you choose may only be available in one of the 2 calibers

Either is plenty sufficient Alexander. Your scope wil depend on conditions and average planned shooting distance. My personal scope choice would be a good 4-16x44 for versatility. You could also go slightly lighter on caliber (308 comes to mind) for lighter recoil as caribou are not as tough as most think. (Just as a by note, Although the lighter calibers will be sufficient and will work fantastic on Caribou, the #1 cartridge for Alaska Residents is the 338 Win Magnum)!

300 with 180 gr bullets or
338 win mag with quality 225 gr bullets.

270 works just as good also. I wouldn't rule that out.

300 WM would be an OK rifle to shoot caribou with (appropriately loaded) if you were a one gun guy. But why would you want to use it on caribou if you have a more appropriate chambering for caribou? Quarter bores, 6.5s .27s, even .308 and '06 mo betta IMHO.
The .300 Win. Mag. has a 60 year old proven history of delivering all the "right stuff" when the right bullet is used. So does the .338 Win. Mag. and the old 30-06. All 3 of them are Alaska's most popular hunting rounds.
I started with a 30-06 in 1966 and have used a .338 Winny for most of the last 40 years and have a new LAW .300 Winny that is unfired. What did I use on the last caribou? The grand old 30-06 and 168 grain Barnes Triple Shocks. The old pre-64 Featherweight ought six is a joy to use and that load offers enough of the 'right stuff" for any Alaskan critter. The very good .300 Winny just has a bit more of it, especially with the heavier bullets.
I am not a fan of multiple loads for a given caliber and tend to use one load for every thing. I also have never killed any thing to dead. Eventually I will spend some time with my new 300. Winny if I can ever decide on the scope it will wear. I am leaning towards the Barnes X 175 or 200 grain LRX bullet.