I have shot brown and grizzly bears in AK, both with a guide and without when I was stationed there in the army. My 2 cents:
1. If you draw blood, you will have to punch your tag. That is the law in AK; don't expect your guide to look the other way if that happens, as he will be in big trouble if the word gets out or you turn out to be a planted state trooper (all game wardens in AK are troopers). For that reason alone, don't worry about the guide shooting "your" bear. Personally, I tell all of my guides and PHs to feel free to unload after my first shot. Alaska guides are more than willing (only had one PH in Africa do it and that was on an elephant that I lung shot but insisted beforehand that he shoot). I simply don't want the animal to suffer.
2. Take a rifle that can weather the elements: do not take something with a finicky trigger, a 700 adjusted too light, etc. - in constant rain, your rifle will rust in places you can't see. I have had trigger issues twice in AK. You would think I would have learned after the first time.
3. Your scope is a bigger consideration than caliber (given you have a 300 Win). Don't show up with a long range rig; you will not be shooting out to 500 yards; your guide will not allow it. I had one guide on Kodiak tell me about a guy with a Gunwerks rifle that said it was guaranteed out of the box to 1000 yards. The guide said he let him take a 500 yard shot - the guy missed the bear completely and ended up going home empty handed.
4. Pay attention to the clothing you bring. IMO, the best is waist high wading pants with a pair of oversized hunting boots, followed by a Gore-Tex type parka, with a Helly Hanson rain parka. The Gore-Tex is for walking in; when glassing you wear the HH if is raining, which it will be more often than not. I actually normally wear a polypro-type shirt when walking and just change out of it quickly when setting up to glass.
5. MOST IMPORTANT: choose your guide/outfit carefully. Someone mentioned Phil Shoemaker; I hunted with him for moose in 2019 but saw more brown bears than moose (after passing several I did shoot one on day 6); great outfit. Cabot Pitts is another good Penn guide; shot a bear in 2017 with him. If you hunt the Penn, make sure your outfit has exclusive rights to their area (like Phil or Cabot); there is a lot of state land used by guides that have great prices but low success rates (I have heard a lot of horror stories in and out of King Salmon). On Kodiak, avoid buying a hunt on what is called a registration hunt, otherwise known as a road hunt. You want to get in a drawing. Finally, realize if you book in areas other than the penn or Kodiak your bear will likely be smaller; north of Bristol Bay the bears are called brown bears but are more like large grizzlies.