Besides the regionals, there are quite a few cargo outfits you can get on with only limited flight time. The biggest hurdle is getting your first 100 to 500 hours of multi-engine experience and your first 1200 to 1500 hours total time. If you can become a CFI-MEI that's one way to build multi time. You can also find opportunities flying owners around or flying clubs.

The academies sell the connection or networking angle, but at any airport you'll be able to make really good contacts with lots of different people in this industry. Flightsafety is probably the best academy with the best reputation, but like everyone said, you can do it more cheaply and in the same amount of time or sooner on your own with a dedicated instructor and FBO.

Best wishes for your aspiring career. The main ingredient we all share is a deep passion for flying that makes us continue to pursue it even though reason and good sense says we shouldn't.