I think if you want to go all the way and consider what should be Essential for any filmmaker to handle just about any kind of need, then the first thing you must have is the basic set of Adobe programs, even if you edit with something else.
Get Photoshop, as it can have useful linking abilities with both AE and Premiere Pro. Or if you'd prefer something else, Corel Painter or even GIMP will be quite helpful for creating elements from footage to use in an effects compositor.
Get After Effects or Nuke, as those seem to be the two most popular compositors. But again, AE is good when you want to pipe things directly from Premiere over to AE and back, and that can save you a lot of time when working through a long sequence of composite shots and color grading.
I think one program that should be a given for everyone is Davinci Resolve, because not only is it currently the most recognized color grading program, but it is completely free (minus 4K and Stereo 3D capabilities), and it has a built-in editor for those looking for a good free program to do minor edits with when they don't have something else. Very powerful tool.
For audio, Pro Tools is perhaps one of the best choices for its support and its broad scope of abilities, but Adobe Audition will handle most of your single track editing needs, which once again can be piped out through Premiere into Audition and back again.
If you want to get into 3D graphics and more complex vfx, then you cannot go wrong with Blender. It creates beautiful renders with a very user-friendly interface. And once again, it is completely free. I'm actually combining Blender with AE and the Video-Copilot plugin, Element 3D, to produce some fantastic shots with almost none of the render wait-time. All of the shadows, highlights, reflections, Ambient-Occlusion, and textural shaders are rendered in real-time: much like a game-engine I imagine. So the effects you can get will be comparable to say the PS3 or even PS4, but that's far better than trying to produce something in Maya, which more often then not, looks like PS2 graphics if you don't spend the time and the effort to get a very detailed model and a very well lit scene.
It's also useful to have a Particle System generator like the Trapcode Suite for AE on hand, as that can be far easier to control and manipulate than a particle generator in Blender, Maya, or Cinema 4D, at least as far as I've seen. And again, it's far more real-time than those other softwares.
And if you want to have a broad spectrum of cheap and affordable environmental assets for your green-screen backgrounds and such, you can't go wrong with DAZ 3D: where every 3D model, character, or environment only costs the purchase price. And then it can be used anytime, anywhere, for commercial and non-commercial reasons, as long as you don't use it in a video-game, and especially if its not open-source. Otherwise, you can use anything you buy in movies, artwork, and anything else 2D based. Which has to be one of the biggest life-saving bargains I have ever seen for Royalty Free assets.
So basically, I think if you have Premiere, After Effects, Photoshop, Element 3D (Video-Copilot), the Trapcode Suite (Red Giant), Adobe Audition, Blender, and DAZ 3D, you're pretty much set to do almost anything.
P.S.
Oh, and make sure you get a digital drawing tablet. Trying to Rotoscope, do color touch-ups, draw effects assets, or other complex gestural things can be an absolute nightmare if you try to only use a mouse.