Studios don't care how many tools you've opened. They care whether a short reel shows weight, timing and a character who's clearly thinking. Learn body mechanics before acting, one main package before three, and leave pipeline scripting for later.
Animated characters for a student short film using Maya.
Animated 14 character shots, including 6 dialogue shots, for a 9-minute student short in Maya; delivered final polish two weeks ahead of the festival deadline.
If you're aiming at feature film or large game studios, start with Maya, because that's what their pipelines and rigs are built around. Blender is free and perfectly good for learning the principles, and some smaller studios use it for production. The principles transfer, so don't lose sleep over the choice. Switching later usually takes a few weeks of getting used to new hotkeys and menus.
For hand-drawn TV work in Toon Boom Harmony, yes. For computer animation, you don't need finished drawings, but quick stick-figure thumbnails and draw-overs make you faster and easier to give notes to.
Short. Recruiters often decide in the first shot or two, so cut anything that isn't your best. Put your strongest body mechanics or acting piece up front and drop older work once you've got better.
Basic rigging helps you understand why a control behaves oddly and how to ask for fixes. Going deep into rigging is a different job, so learn enough to diagnose problems, then spend the rest of your time animating.