Main Programs:
Furnace tracker: The premium free tracker for any system of your choosing. While the interface is not the most approachable, it's utility for FM chips cannot be understated.
Deflemask (free legacy version): A more bare version of the paid tracker program, Deflemask. This is what I started out making songs on, my 1st to 13th releases (Courtroom Lounge to Cheap Shop). Moderately easier to approach, but has bugs that will not be fixed as it no longer receives support. Would advise sticking to Furnace for its bug support and community.
Audacity: A must have for the modern music creator, Audacity is a feature-rich and completely free audio editor.
OpenMPT: Sample-based tracker compatible with a wide range of file formats. Have not used in composing myself, but popular for those preferring sampled music like released on DOS and SNES.
VGMusic Studio: Music player and visualizer for GBA and Nintendo DS music. I don't compose using it, but have found it helpful to separate music released for those systems by channel.
BambooTracker: A tracker focused on the YM2608 "OPNA" chip (similar FM and PSG capabilities to the YM2612, plus 6 dedicated rhythm sample channels and a dedicated sample playback channel). Jake Kaufman composed the excellent Shovel Knight Dig OST using BambooTracker, and has made his modules available from the album Bandcamp page; alternatively, you can download it by clicking here.
Instrument tools:
Vgm2pre: Tool for ripping YM2612 instruments from .vgm files.
Dexed: A synth program imitating the Yamaha DX7 keyboard. A handy virtual tool to use alongside the pdf below.
FM Theory and Applications: Guidebook on FM for music written by its inventor, John Chowning. This level of understanding is definitely NOT required to start making songs, but can provide valuable depth to inform instrument design when one feels ready.
(Not sure I feel ready, ha. Haven't finished reading the guidebook myself)