untreated new wood fence
Unless it's kiln dried wood, the problem you may run into is the moisture content of the wood. You can prime and paint all you want, but it will blister and bubble as soon as the sun hits it.
I had a 2x2 redwood end post that was so wet ("cut last Tuesday," as they say) that took at least 6 months before it dried out sufficiently. This was the worst case one; the other two posts took at least 4 months.
Looking back, I would buy a moisture meter and test them first. Other wise it's and endless loop of: sand, prime, paint, and curse.