If weight is an issue, you're probably better off with a light red dot...Aimpoint T1/H1 comes to mind here, or open sights. Other than that, the scope should reflect the long-range capability of the .308 round and have decent magnification. Many members here use the Bushnell 3200 10x40 mildot.
For hunting, a short-barrelled rifle with an ARMS 18 mount and a simple Burris Fast-Fire II. Very light and relatively inexpensive.
I have a 10x40 mildot bushnell on mine with a ARMS mount, however I am thinking about putting on a Millett DMS 1-4x24 and getting the barrel chopped and recrowned, to make the rifle into a more lighter easier to carry rifle for hunting deer.
I use an IER(intermediate eye relief) Burris 2.75X scout scope for everything. It even does V-bulls out to 500m for Service Match and 15m CQB ranges easily. I use it for hunting in the thick Quebec bush for the Deer season.
If were to put regular scope on it, it would a 1-4X or 2.5-10X of any brand I can afford (which is not much) with a Milrad or Mildot reticle.
Tön