Ghost shrimp are fine, but after maintaining a frogfish on live foods for a period of time, I prefer to have them on a frozen diet. Either frozen or live, the diet should be varied. IMO, some considerations for maintaining a diet of live food are the long term expense, the potential for the source to dry up leaving you without food for your fish (even temporarily), and the potential for introducing pathogens. I maintained a frogfish on live foods exclusively for several months (the aforementioned A. coccineus, with me for 19 months now). I had several sources for live food, both locally and mail order, and was let down on more than one occassion. I established a breeding population of peppermint shrimp, which met with mild success, and then got too busy, and finally converted exclusively to frozen. I can't help but recommend you save yourself the trouble and go with a frozen diet if you can. Now if your fish won't take it, it's a different story (but that is pretty rare IME).
Whatever you feed, I still recommend using a net or tongs so that you can target feed your fish and ensure that he is getting his meals. While it is sometimes fun to watch the hunt of live food, and I do give live treats occasionally, it is also fun to get to interact with your fish yourself. People love to come to my house and watch the frogfish get fed. Two of mine always put on a good show, with lures and everything. People look at my seahorses and say, "oh, that's nice," and walk away. They stand at the frogfish tanks and ask lots of questions, not the least of which is, "why would you want a pet that ugly?"
