The game has changed significantly even since I graduated in 2011.
It's not just as simple as Federal/Public vs. Private, though. There's Federal Perkins Loans, Subsidized Stafford, and Unsubsidized Stafford for undergrad, each with their slightly treatment and regulations. On top of that, there's different programs for graduate programs. A more in-depth conversation on your exact situation is really reliant on your FAFSA results/university's financial aid offerings though.
Whatever you, be sure to only take out as little as necessary. No need to be saddled with more debt just because you didn't want to work part time during the school year. That'll hurt much more in the long run.