Between the Sofitel and JW Marriott both are nice hotels with good beach access. the Sofitel is across the street from the Copacabana Fort and around the corner from Siri Mole, possibly the finest northeastern (Bahia) food to be found. The specialities are seafood in spicy stews. It's been one of my favourites for more than thirty years. The JW Marriott is smaller, but has brat views from the executive lounge and the rooftop pool. A;although the Sofitel has one of the best French restaurants in the city i would not recommend food at the JW Marriott.
The Copacabana Palace is another great option, the grande dame of Rio de Janeiro.
Truth be told Copacabana is the longest beach and has the most varied activity. Many Cariocas think it is "the best" of Zona Sul. Ipanema is smaller, Leblon smaller yet but both of them are less varied and more upscale than is Copcabana.
There are endless options of great restaurants and wonderful things to do and see. In these threads are lots of information. If you'll tell us about your interests and preferences, as well as a bit of information about yourself we'll do our best to help advise you.
There are quite a few regular visitors to Rio on this board, and a few of us live in Rio ourselves and/or are Brazilian.
So, explicitly answering your questions:
1. Truly, the best beach in Zona Sul is a subjective choice. I choose Copacabana. note: my family has lived in Copacabana for more than 50 years, I met my spouse there, among other things so you might consider me to be biased. However, I have other relatives living in Ipanema and Leblon and they're nice too.
2. Were i in your situation as you've described it I would stay in one of the two you mentioned or the Copacabana Palace.
3. No! Stay on a beach in Zona Sul for your first four day visit. Anywhere else is for subsequent visits.
4. For food there are countless options ranging form some of the finest French and Italian food anywhere, outstanding Japanese (there are many millions of Brazilian-Japanese), pizzerias beyond compare, not to mention Brazilian regional cuisine for all regions. If you tell us what you like we'll make recommendations. Also if you need guidance we can advise you of regional Brazlian specialities.
Just to claify when arrive BA FC, your baggage will not be in the hall very long. Baggage handling at GIG is quite good.