KTC,
Just my two cents worth, but have your wife shoot the gun that she is most confident/comfortable with regardless of whether it is the 300 or the 270. Just shoot primo bullets (I like the Barnes 3X) and be able to hit exactly where she aims. An accurate shot with a smaller caliber is much better than a marginal hit with a big bore.
I am generally an advocate of putting one through the boiler room, but on goats or sheep where one step can result in a mangled trophy or even an irretrievable animal, I want to anchor them.
A goat's skeletal system is a little different than deer and elk and to really anchor them, you will shoot the shoulder a little higher than you would think and break the spine as well.
An Alaskan guide friend of mine who has guided many goat hunters told me to envision a line from the base of the ear to the base of the tail and then a second line running vertically right up the middle of the front leg/shoulder and shooting the goat at the intersection of the two lines. This shot destroys at least one shoulder and the spine, resulting in an instantly immobilized goat. He told me this works for any ethical angle shot (broadside/quartering away/towards-even with steeply angled shots).
I shot my only goat using his advice at approximately 300 yards on an uphill, quartering away angle. I watched it from 70 yards on out. I had to wait for the animal to stand above a rock that would stop it from falling off the cliff after the shot and get to a place that I could retrieve it after the shot.
It turned semi-broadside above a small boulder and I hit it exactly as I described above and it literally crumpled up around the small boulder. After the shot, I watched it with another round ready if it was necessary. The goat was stiffly wrapped around the boulder. When it went limp (dead), it ever so slowly started to slide around the boulder and slide towards a chute, but it hung up.
The attached picture shows the rock and the chute, but it does not do justice to how brutally steep it was up there. If that goat had taken just one step, I would have been retrieving it 1000 feet lower than where it was standing.
Also, wait as long as possible in your season to allow the goat to grow its winter hair. The trophy is not the 9-10 inch horns, but the awesome hair. My goat hunt was one of my absolute favorite hunts, due to how tough it is to get around where they live, the incredible scenary and the effort that I had to put forth. Enjoy the whole experience, it is too hard to draw a tag not to take advantage of that incredible adventure.
Good luck to your wife and post some pictures.
WyMo