Software
Screenwriting - Adobe Story is free software that let's you write storyboards without worrying about formatting.
Editing - Adobe Premier is an industry standard
Storyboarding - lots of cheap software to help so you don't have to draw out sketches by hand.
Music - any music composition software that will let you write music score and edit narratives and sound effects.
Equipment
Camera - DSLRs are a good way to start on a budget.
Mics - get a short shotgun with wind protection. Mic holder stick would be good to have too.
Shoulder grip - so you could place a camera on your shoulder and not have it be jittery.
Camera slider and rails - so you could slide through a shot with a camera smoothly.
Camera tripod.
Greenscreen - so you could create locations you don't have access to for real.
Lights - one hard light, one diffussion light to soften the hard light, and a background light behind an actor.