As noted, each rifle behaves somewhat differently with any particular ammo load. I would suggest that you get a box of Federal Gold Medal Match or Black Hills Match ammo in the bullet weight you want to use (e.g., 168gr Sierra Match King bullet) to establish a baseline for that rifle's expected performance. In my experience, Fed GMM or BHM is a pretty good accuracy load for most rifles.
Having determined the rifle's basic level of performance, I would suggest a basic hunting load like Remington CoreLokt, Winchester Powerpoint, Federal Fusion or the like loaded with 165-168gr bullets. Compare your groups with the standard loads against the match loads; they will be a bit larger, but you may get lucky. As an example, I get 3-shot groups with my match hand loads in my Ruger No. 1 in 6.5x55 SE that typically measure 0.5-0.75" at 100 yds. When I tried a box of 140gr Rem CoreLokts, I got several groups between 0.75-1.0" and a box of Prvi Partizan 140gr Soft Points that gave me 1.0-1.5" groups.
Next, if you're not satisfied (but a deer's vitals are the size of a 9" pie plate so looking for better than 1-2 MOA is really unnecessary), try a few different premium hunting loads. I always try Federal Premiums with Barnes TSX or TTSX, Nosler AccuBonds or Partitions and Sierra GameKings and Hornady Customs, again in comparable bullet weights. Nosler also produces excellent hunting ammo with their line of bullets. Since more deer have been killed with basic Rem CoreLokts than just about anything else, premium bullets are not really required for them. Nevertheless, you may want to try them, selecting the ones your rifle likes best. I'm a hand loader and I like to tinker so I continually try to develop optimal loads for each rifle I use and each type of use I plan...to me that's the fun of hand loading and shooting practice.
I tend to use 150gr bullets for Whitetail, 168gr bullets for Mule deer and 168gr or 180gr for elk. Other hunters have other preferences; sample their opinions in various fora (I like to add to my knowledge from others' experiences...one of my favorites is Craig Boddington). I think you've made a great choice of rifle. I have two Ruger 77 Hawkeye RSIs, in .308 and .270 as well as my No. 1 in 6.5x55 SE. They're accurate, reliable, light and well balanced with Leupy 2.5-8X36 scopes...I enjoy all three for hunting and all three are enough rifle for what I mostly try to do.
Good luck,
FH