what is essential depends on how you work and what you produce. here is what i use:
sketchup 8 (for initial modelling)
su2kt (a sketchup script for exporting to kerkythea xml files)
jkt2obj (a batch script for converting those xml files to obj files)
blender(for finishing models, animating and rendering)
paint(ordinary microsoft paint, for basic picture editing)
gimp(for most of the image editing tasks)
for a short while i also used, but no longer use
windows movie maker (for final sequencing of clips into a finished video and adding sound clips to silent videos)
wax 2.0 (for greenscreening and some compositing)
i believe both wax 2.0 and windows movie maker can be replaced using various features within blender, but there are some things i did with both that i have not tried since i stopped using them.
as other useful software to have
vlc (for playing videos)
google chrome(for web browsing)
notepad (for quickly holding text i want to copy/save/etc)
for maths i just use my head, a scientific calculator and some old piles of paper, i also use them for writing notes to myself and drafting up quick concept sketches. if i’m looking for examples of a complex phenomena i’m trying to depict i hunt for videos of it on youtube. for sound effects i usually record things myself with a microphone but i also have some old sound clips lying around which i play over each other to create other sounds.
really what you need depends on exactly what your desired end product is and what your workflow is.