1) I have the same rifle in 300wsm. My Tikka, while I can dial in excellent 165gn bullets (Federal Trophy Bonded Tipped, Hornady GMX), absolutely prefers 175-180gn class bullets, particularly the 175gn Berger VLD Hunting which killed the elk below. Hit high on the shoulder (my bad) but jellied the lungs and dropped her in 20 yards. Although it is not "high end" ammo, I would seriously considering trying out how it shoots the Federal Fusion 180gn factory ammo. The 100s of reviews from users can attest to the stuff.
2) Like JD126 said, it is sad to have to rely on Winchester brass, with a rate of roughly 5 pieces per 50 inspected as bad seen in my experience with both rifle and handgun brass. I went with getting Norma brass thru Midway and it's been very consistent. Budsgunshop.com and Brownell's are also good sources.
3) I use CCI 250 magnum primers for everything.
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One key piece of advice for any Tikka T3 Lite in heavier calibers! Get a Limbsaver model 10011 recoil pad. Try Walmart.com or Ebay to get it for about $25. It is a HUGE improvement over the stock pad, custom fit and takes about 2 mins to install. I will venture to say that it will remove recoil as a factor in your shooting. Cheers and enjoy this elk killer.