I compete in the UK F Class League and stalk "a bit"
If you want a dual purpose rifle, you will not be looking at Open class, rather FTR, limited to 308 or 223 calibre.
I say this because Open class is an arms race, high end kit, 7mm magnums or 284 and very, very close tolerances.....not ideal for dragging to the forest or hill.
Forget the 6.5 calibres - they just cannot hold it against the 7mm's in competition.
As you want a deer legal rifle you now limit the option to 308.
Most competative 308 F Class shooters have single shot actions, full F Class style stocks and custom or dedicated F Class bipods.
You could use a sporter style stock or tactical with the latter type bipod and appropriate fitment.
If you use a factory gun, you wont be competative - unless of course you can read the wind to a mph at 1000, 1100 and 1200 yds and are a gifted shot. (I suppose the latter applies to using 308 anyway)
Sorry, thats just how it is.
You could start with a factory rifle, but the rifle would be the limiting factor to success.
For what its worth, you could use a Barnard SM (repeater), or BAT, or and other custom action, a match grade barrel and A5 stock and you'd be on the way.
However, I think its a big ask especially when you consider you want to be using at least 155, 175 or 200 grainers which means a long barrel (for velocity) and appropriate twist rate to get the bullets on target at range.
My own opinion is two rifles, one for each discipline and keep em separate.
Just my 2p
Oh, BTW
My F Class rifle is a 7mm/270 WSM, the stalking guns are 25-06, 6.5x284 and 308 respectively.