I just came in from working up a new rifle to ready it for the range to see what it will do and found your question. I'll tell you what I just did for starts.
clean the barrel
remove stock
adjust trigger to 3#
replace stock without final tightening and leaving the rear action screw loose
tighten some the front screw and bang the butt on the ground to set the recoil lug against the stock
tighten the front screw to 40 inchpounds (65 inchpounds if pillar or glass bedded)
tighten the rear screw to same
That is where I start
Matt n Barb's list is all very well, but most of these are very small influences and are not readily doable. Still, I think your rifle will tighten up by half. You should, with that bore size, strive for 1/2" at 100 yards. Most factory cartridges, especially the premium brands, will shoot as good as reloads, but you will have to find the brand that works best in your gun to get reload performance.
From the MNB list above, the wind and your shooting ability will be the biggest influences on your shooting, but I think your limiting factor currently is the scope. I had a "$100" tasco on my Remington 700 30-06 that would do 1.5 MOA (not bad for a sporter in that caliber) but with flyers in every group. Any adjustment I did was very imprecise and variable as to the POI. I replaced the tasco with a Leupold Vari-X II (not even their top of the line Vari-X III) 3x9. My groups went to 1 MOA and were consistant without flyers. If it is not because of your shooting, and it shouldn't be if you are shooting of sandbags, the irratic shots in your groups are from the reticle not seating consistantly on the erector springs after each shot. Buy, borrow or steal a quality scope (Leupold, Kahles, Swarovski, Zeiss, Nightforce, or Burris Signature line) and see if this helps. I like to move my windage and elevations in only one direction to eliminate any backlash from my adjustments. To be consistant, I move in the direction of the up and right arrows (or whatever arrows are marked on the scope) For example, if I need to move my POI down 1 inch, I move it down eight clicks (1/4" per click) and then up four so that I alway approach the adjustment from one direction. In this case, up.
Give it a try and see what happens. Hopefully, it will put the rest of the list off your priorities. As a rule of thumb, you should spend as much on your scope as you do your rifle. Currently, the consensus among the shooters I lurk with, the Bushnell 3200 and 4200 lines are the mostest for the leastest.