Which antenna 2.4 or 5Ghz for range extender.

Some do both, but it is a jack of all trades, master of none. If you are going for peak gain, you need one of each. All of the campground wifi I have ever been to were 2.4. I prefer 5g, as there is usually no one on it. For example, at my office there are ~10 2.4 access points I can pick up from my desk, but only 2 5g, both are mine. At home I am looking at 15 2.4 access points, 3 are mine (1 is Comcast, one is my adt pulse, one is my outside access point). My access point is the only 5.8 I can pick up from here.

2.4 travels farther, and penetrates walls, trees, etc better. 5.8 is far faster, as you don't have to share the airwaves with anyone usually)