The .308 will take down any of your wanted species. A recommendation is to take a premium bullet and place it in the vitals.
Last year, I loaded some 140 gr Nosler Partitions for my 7mm-08 behind RL-15 for a trip to RSA last year. I ended up not taking any game with this load as I used my 300 Win Mag the entire trip. However, I did take an addax and Texas dall ram two weeks ago. The addax was about 125 yards away and the ram was 90.5 yards away. The addax stumbled about 40 yards before going down as the shot was thru the lungs. The ram was DRT. Both shots complete pass thrus.
Remember the vitals are further forward then N.A. game. Put the bullet thru the shoulder! Then, smile pretty for the camera!
Good luck!