There are lots of posts concerning favorite powders for the 308, and is a pretty good place to begin. Favorite powders are IMR4064, IMR4895, Reloader 15, Varget, and a few others. Mostly, I find that accuracy depends more upon the bullet than your powder selection. When I am choosing a powder for a caliber, I look to see which gives me the fastest velocity in the starting load column, and normally there will be 3 to 5 powders near each other.
To begin loading, I use the bullet manufacturers suggested starting charge, primers and overall length. Then try upping the powder charge in 2 or 3 grain increments until I see the groups shrink, using 10 to 20 shots each-that takes away flukes which might be seen in 3 or 5 shot groups. When I find the charge weight it likes, I then begin changing the overall length .005 to .010 longer to dial it in.
Some like to fully resize their cases, and others neck size depending on how warm the load is. If you find your best groups near suggested maximums, I recommend setting up your resizing die to push the shoulder back just a few thousandths. It works the brass less and will chamber easily. I also recommend you trim your brass initially to the same length and re trim when it gets close to the max case length. If you are going to use military brass, keep the loads 1.5 to 2.0 grains less than the maximum charge weight listed-military cases are generally thicker and so have less capacity. Winchester brass and Lapua seem to be among the 2 most favored, although I am trying out Hornady Match brass with good results too.
For target work, the Sierra Match King is a pretty forgiving bullet in the 168 to 175 grain weights with all of the above in play.