KDM,
Valid questions! I'm surprised no one has given you any input yet.
It's a fine rifle, that always needs a bit of tuning up. The actions can be slicked up with some JB bore paste, and about a thousand cycles back and forth. Don't get the paste in the locking lugs, or turn the bolt as you work it.
The .375 is not as prone to crack it's stock as the larger bores, but it still deserves to be glass bedded, and a section of steel "all-thread" down through the wrist of the stock is a good idea. Leave a little clearance between the end of the tang, and the stock. Not much, just enough so the tang doesn't hammer the stock during recoil.
As to recoil, no big deal. It is a large rifle, with sufficient LOP, and good ergonomics. It is more of a big push, than a sharp jab. If you reload, and I suggest you do, start with some light bullets, maybe a Speer 235 grn., and a light powder charge. Get used to that, then work your way up to full house loads with 270 or 300 grn. bullets. You are going to enjoy this rifle!
By the way, in my experience with these rifles, they always shoot high. You can contact CZ at, gunsmith@cz.com to order taller front sight inserts. Chances are that you will want the tallest one, which is a number 14. It may, or may not be high enough for you.
Good shootin' to ya!