Your project sounds very interesting.
A few quick tips regarding how to go about it (regarding whether or not you should shoot it yourself; you might want to have a pro start shooting it and later, when you've learned how to shoot, you could continue by yourself).
Identify the characters, the people, men and women that you want to shoot;
Research all the information you can find about the community that interest you: this means research archives of local newspapers, and identify and read some books dealing with these issues.
A book that comes to my mind is: Finding Manana: A Memoir of a Cuban Exodus (Paperback)
by Mirta Ojito
If I remember correctly, she's working on a documentary based on her book.
You may find some useful information here:
2) Visit and research the neighborhood. I would assume that there is a "Little Havana" in Miami. Visit the neighborhood, reserach everyhting about it, discover who some of the most important members of the community are, when any particular religious or other festivities take place, etc.
3) Shoot all of the above.
4) identify 4 or 5 interesting characters. get to know them, interview them, shoot them at work and with their families, get photos, visit with them for several months/one year.
5) Decide what kind of doc you want to build with the material you are gathering.
6) Build your doc around the personal stories of these 4 or 5 people, interweaving blocks about the community. The fact that the situation in Cuba is moving and that this is an election year will give you great topics and great video to interweave withe stories of your 4 or 5 protagonists.
Re your second question, wireless lavalier mics are very good to interview people. I would suggest you might be interested in the Sennheiser Evolution G2 100 series; it has a good price/value ratio.