Relatively few meese to be found near Mishawawka, IN. For WT deer, .25-06 up through all the 7mms will work fine if you don't like .30 cals. I do a fair amount of shooting with thin profile ss barrels...they're fine for the first three shots. If you need more, spend more range time.
If you're serious about moose, a fast .30 through .338 WM are good choices...and if you're gonna be in places where you might stumble across a brown bear while looking for his herbivorous friends, a .375 Ruger or H&H or .416 Ruger might be a good choice.
FH
EDIT: I just read your second post. I have a reasonably new (2009) Savage 116 FHSAK with accutrigger and accustock in .30-06...it delivers to <0.7 MOA out to 300 yds off a Caldwell Leadsled with Federal GMM. I'm working up loads with a variety of powders...preliminary indications suggest this Savage will deliver 0.5 MOA. Every company makes a lemon now and then...1-1/2 MOA is good hunting performance...that's 4-5/8" at 300 yds. I have a few M1 Garands that will only do 2-3 MOA...with M2 ball and I'd bet my life on them.
My next will be a Savage 111 LRH in either .25-06 or 6.5x284. YMMV