In case you haven't purchased the rifle yet, DON'T. I don't hate the 308 or Rem but there are now so many better choices.
Assuming the factory Rem would cost upwards of $1000, you have so many options today especially in the factory rifle. You can spin on a match barrel for that type of coin too.
First off, get a better cartridge. Unless dictated to use the 308, ie TR/Palma class, it is the worse ballistic vs recoil rd that can fit in a short action. 243, 260, 7-08 are head and shoulders better ballistically and do so with up to 50% less recoil.
In comp shooting, reducing recoil is paramount as it lowers shooter fatigue which improves concentration and your score.
If you must use the 308, then the 223 in a fast twist will do the same thing with 1/4 the recoil and 1/2 the cost. Trigger time is everything in LR shooting. That costs money and shoulder wear and tear. Just look at the domination of the 223 in all service rifle shoots in the US. It works!!!!
If you don't mind a 2lbs trigger (personally, I would choose something as light as possible), a Savage 12FV w/Accutrigger in 243 or 7-08 would be just about perfect. Ditch the stock and pick up a proper Prone/Fclass stock from Ian R. Stock fit matters enormously and the HS offers little more then the orig Savage or Rem, alum bed aside.
You will find the Mcm A5 or SAKO TRG Or AI stock shape to be far more comfortable to shoot off bipods. I prefer thumbholes stocks but a vertical pistol grip really helps to reduce wrist fatigue which improves trigger control. In F class, you do alot of shooting so you better be comfy and on the ball. Wiggling around or getting sore anything is going to cost you points.
As one very good F class shooter told me, when he gets set up prone and on the bipod, he is so comfy that he can just fall asleep.
If handy with tools, the orig Savage stock can be rebuilt to fit you. Probably the best way to get a proper stock fit. Take the time and view some pics of stocks used in competition. Look at all the moveable parts so that head/eye/shoulder and body can be kept in proper alignment. You become the bench and if you are always wobbling/shifting, thanks for playing...
For optics, a 10X will be on the low side. The nikon is a superb scope but for comp use having 16X or higher is not a bad thing. Also, mil dots or some sort of marked reticle will become an enormous aid for quick doping and shot adjustment. Chasing turrents is a huge source of error and driver fatigue.
Watch the flags and conditions, not the dials on your scope. I dial only when changing range. Windage is done using the 'dots'.
Pay attention to ring height. Play around until you can look through the scope without bobbing your head on the stock. You should be able to get into position with your eyes closed, open your eye and have perfect scope field of view.
Get out there and practise, practise, then practise a whole lot more. A well tuned Savage or Rem will shoot 3/4 to 1/2 MOA which is more then competitive. However, few drivers can keep up that level of accuracy over the course of a day.
Keep fit, well hydrated, and focused behind a good fitting rifle with a crisp light trigger and clear trustworthy optics. That alone is worth more then any techie bling you might want to add to your rifle.
Jerry