Just to take your thoughts on Tikka in 300 WM; the mag limit is 3.370”. Hammer developed their 174 gr. Hammer Hunter with short mag lengths in mind. My T3X shoots the 174’s loaded at mag length very well with1/2” groups the norm using 76 gr. of H4831sc in Peterson cases and Fed 215M match primers. Velocity is 3050. RL 22 works just as well @3100 FPS, but is temp sensitive.There was a similar thread posted last month and so I will just copy and paste my reply to that thread as it seems to fit yours as well. He had the Savage High Country as a possibility as well.
There have been a lot of answers to your questions in this thread but no one has brought up the limitations of the platforms. It seems that some of the posters are not exactly doing you a service with their answers. I don't pretend to have all the answers but I hope I can give you some things to think about and help you with your decisions.
As far as the Bergara, I don't have experience with them but you do.(ETA: The other poster did.)
Tikka: You said you wanted a 300 WM. Unless something has changed, and it has with their twist rates going to 1:10 so maybe it has, their mag box length is very short as they did not make a true long action last time I checked. You are really limiting yourself to short bullets or really jamming the long bullets back into the case...If you are thinking about going with a short action cartridge Tikka is a great answer though. 300WSM....go for it.
Savage High Country: I was about to get one of these, but while doing the research I found that the OAL length is again limited. Not near as much as the Tikka but still limited, and with the bottom bolt release it may be harder to find magazine boxes to extend that. I will say that barrel changes are awesome and of the choices I would probably take this, if you are getting the WM. There are other Savages as well that you could look at, like the 110 Tactical. I believe it takes AICS mags at 3.850.
Browning: If you are the kind of guy who goes out and shoots 20rnds a year they are good to go. I have had multiple Browning rifles and they are very nice. I would not buy another one. I basically think that they are a throw away rifle, as unless you are friends with a gunsmith or can do it yourself with your own lathe etc the barrel replacement process is prohibitive. You might as well buy a new rifle, and finding a gunsmith to even work on them is a pain in the ***. My Brownings now sit in the safe doing nothing. A 300WM will eat a barrel in around 1200 to 1600rnds. Do the math and see how many years that will last you. That's why I said what I did in the first sentence.
If you can, I would save up and spend the money on a custom action that you can put prefit barrels on yourself. My last rifle is a Zermatt Arms Origin. I can switch bolt heads and barrels easily. Just some things to think about.