Apart from your acoustic space and the player or person you're trying to record, one of the most important choices you can make is what microphone to use. I recommend starting with a standard dynamic microphone like a Shure SM57 ($108) or SM58 ($109) and moving up to a larger diaphragm condenser mic like the Audio-Technica AT2020 ($119) for instruments like acoustic guitar, vocals, and piano (as well as essentially everything else you could want to record) when you have a bit more cash to do so. Down the line, you can explore things like ribbon microphones and small diaphragm condensers, but a simple dynamic/condenser pair is more than enough to make the vast majority of records, so long as you're not recording a drum kit.
If you are recording a drum kit? I highly recommend just starting with a microphone pack like this one from AKG ($481). They aren't the highest-end mics on the planet, but they're more than enough to get good drum sounds when first starting out, so long as you can play and tune your drums the way you like them.
For headphones, I recommend you snag a nice wired pair of closed-back over-ears like those from Beyerdynamic or Sony. These allow less bleed from what you're listening to (and recording over) into the microphone.
As for cables and stands: They really don't matter that much if you're not constantly messing with them. I recommend getting either colored cables or ones with colored ends, because it really helps visually remind you what is going where when you have lots of cables going everywhere. For stands? I actually love a simple swing-top desktop mic stand ($22) if I'm just recording vocals, percussion, or acoustic guitars. If I need something for a heavier mic or for a more open space, I prefer K&M stands ($102). They're a bit more expensive than Amazon specials, but they're very durable; I have yet to break one.