You can spend a lot of money on audio equipment, but I had used a very simple set-up on a lot of my productions – including a feature-length film – with great results. It consisted of the Zoom H4 portable audio recorder, and the RODE NTG-2 shotgun microphone (with a boompole, blimp, windscreen, etc.).
Since then, I have upgraded to newer versions of this recorder and mic. Here is what I currently use
If you want an even better audio recorder, with 8 tracks, a safety track, and other great features, then I would get this one
Sometimes you cannot use a shotgun mic in a scene, and you’re better off using wireless lav microphones. Although some people complain about the reliability of wireless microphones, the following kit from Rode has never failed me. I strongly recommend it.
I have a post where I talk more in depth about my audio set-up on films. It also lists all the audio accessories I use. You can check it out here.
I also have a video where I directly compare these three portable audio recorders: Zoom H6, Zoom H5 and Tascam DR-40. You can check out my tests here.