Like most things...it depends. For mono vs braid, if you plan on fishing in the "congo line", where you are elbow to elbow with other fisherman, you will make a lot of enemies really fast if you're using braid. Braid will cut through mono in an instant, and other fishermen tend not to like that.
Lure size/construction will depend on the fish and the conditions. I personally RARELY use topwater in the surf, and I never use bucktails. I never see anyone using fake eel either.
As others have mentioned, you will need to learn to read the surf and the shore to find good spots to fish. being able to cast a mile is not a necessity, but it is helpful.
Being able to cast long distances can indeed be helpful. I remember fishing one day years ago at the Ocean City jetty, and knocking the hell out of some good sized bluefish. That was because, through nothing but having the equipment to be able to cast further than the others there, I was the only one there who was able to reach them.