You're on the right track. Rarely will you be hired, if you try to get a job in production, because you have a film school degree. I'm not saying going to film school is useless, and you certainly can learn wonderful things, but the best teacher for a filmmaker lies in the making of the film, or more correctly, films. Fortunately, we have grown into the digital age, and anyone can be a filmmaker, with cameras and editing systems becoming very affordable. Contrast with trying to be a filmmaker in the 1950s-1980s, where you would be at the mercy of buying expensive film stock and at the mercy of post production facilites.
Since you are interested in being primarily a producer (leaving out your other desire of being a screenwriter, something you can do entirely on your own), learning the skills of filmmaking becomes even less important. (But, of course, a good producer must be extremely knowledgeable about the dirty work that goes into all aspects of making a film.) Getting into business would be a wise choice. Many who run the studios are ex-lawyers. Of course, many of these idiots know diddly-squat about films, which is one reason why many Hollywood films are uninspiring.
You should aim for the top, but be aware that the film business has become very unfriendly for independent filmmakers. There was a time when winning awards in festivals would get you going, but many of the festivals are now exercises in corruption (festival managers are in it for the profit) and kowtow to the studios (in other words, in days of old, your good quality film would give you a good shot of being chosen for the festival. Now the quality of your film can often be irrelevant, because the few festival slots are granted to the powerbrokers like Miramax).
In addition, the most essential criterion is not getting the film made, as nightmarish as it can be to get a (feature) film made. Getting the film distributed is the key. Today, supply outweighs demand (now that everyone is a filmmaker), and many of the smaller distributors have dried up. Your plans are great, but your woes won't end with getting the financing and getting the film made, as difficult as these processes are. The film business, always uncompromising, has become increasingly tough -- with power now centered into the hands of fewer and fewer players.
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