It depends what you are looking for really. Marmaris is a very big resort, loud, busy, lively. Gumbet is a lot smaller but still lively with a nice beach and within easy reach of Bodrum for a change of scenery, shopping and to explore around the peninsular.
I lived in Gumbet and have only visited Marmaris once for a short time so maybe I am a bit biased but I much prefer Gumbet and Bodrum.
I wouldn't personally recommend AI as Turkey is such a great place to go out and about it seems a shame to be tied to the hotel. You can find very resonable and good food everywhere and it is fun to go out and try new places. There are some lovely apartments in Gumbet some of my recommendations are: Queens Resort, Ozukara I or II, Siesta Beach, Jasmin Beach, Tropicana Beach but there are loads more there too.
It is easy to get into Bodrum by dolmus, it takes about 20 minues and there are great shops, bars, restaurants plus a weekly market and places of interest if you facny a bit of culture. From there you can also take a dolmus to numerous places around the peninsular, small resorts, lovely beaches, fishing villages etc.
Wherever you go in Turkey though I am sure you have a good time, it is a beautiful country and the people are so friendly. Just ask if you want to know anything else.
Kedi