I have a really different take from everyone else here. As a working pro, I like used gear and think good 'enough' quality audio for short films in non-professional environments can be achieved cheaply and easily.
Specifically, I would do this:
- Buy a used mic. I bought an ECM 674 for $70 used. Because no-one has ever heard of this mic, they are ignored, really cheap used and the built-in high pass filter helps hugely with decent-enough sound (for what you want) even though you don't know what it is.
- Get a used recorder. Now, mine died on me when I went pro because they take a pounding in a professional environment but for shorts where they don't get much use, they're fine. Get a Tascam Dr-100 Mk2 or in a pinch, a 60D Mk2. Maybe a Fostex FR2-le as they're excellent but ancient and they will eventually die on you (mine did) and again, $150 USD.
- Get a cheap boompole and shockmount. $100. There are loads of Rodes out there.
- Buy a blimp and deadcat if you're recording sound outside. Buy used and do not cut corners. $300 USD for this.
- Get some headphones. If you don't have any, borrow some from a friend.
So total is $620 USD if you're filming outside and $320 USD if you're filming inside. So write stuff where there is absolutely minimal dialogue outside and you'll save yourself $$$$.
Next bit: Practice with the kit. Practice, practice, practice. Hold the mic as close to the subject's mouth as possible.
This is the minimum budget for OK sound for low-budget shorts. I am a generalist so my kit is around $3,000 USD for recording a single person talking on an interview which most sound pros would think is pretty cheap. But then again, I have a small, production house so have to think both sound and camera and put money where it's needed.
I think a lot of those don't make sense in the context of 2019. Because options have expanded and technology has advanced.
I'd say go with: Zoom F4 + Aliexpress Carbon Boom Pole + Rode Blimp + Deity S Mic 2 (for outdoors, get an AT4053b with INV-7 for indoors).
That is the bare bare bare minimum that anybody should be considering, even if they're just a "generalist" or a 1st year film student.
HOWEVER.... if you're literally begging on the streets at the moment for food and living under a bridge, then you could consider: 2ndhand Tascam DR60D, Aliexpress Alu Boom Pole, Marantz Blimp, secondhand Rode NTG1 (for outdoors, for indoors get a Samson C02 with a INV-7)
However I'd say if you're sleeping under a bridge at the moment then you've got bigger issues to worry about than your sound kit!