.270 would be a great caliber. Zero it in for 200 yards though. Many reasons, but goats like to be a long ways away. Zero'd at 200, the .270 130 grain will be in the kill zone for anything 250 and under. Even at 300 yards only drops 6.4" So you hold it 3-4 inches high on the hide and BAM! You got meat in the freezer. Also, it is a very popular and common caliber and would be easy to find in the remote areas you may end up in. It also loads up to 150 grains which can be used for close (100 - 200 yards) Elk hunting. Also, easier on the shoulder (kids, females) than the .06 or 7mm Mag.

As far as gun/scope . . . I personally would spend $100.00 on the gun, and $400.00 on the scope! Good optics my frriend will make or break your hunt. Does Walmart even sell a bad gun? I don't think so. I lean towards the Savage models. Very close tolerances and very affordable. Don't go cheap on the scope. A variable up to 12 power is highly recommended for long range goat shooting. Nothing worse than having that 14+" goat out so far that your crosshairs cover up the target! It happens.