Here are some websites where I've seen plenty of self-published works. All of them have these in common:
Publication price: All of them are free. No fees required! Better make accounts for them, though.
Impact factor: None of them will publicize your music anywhere near particularly hard. It's your job to publicize the links to your accounts with these websites.
Publication criteria: Anyone with an account can submit to these websites.
Now here are the websites:
Type of recording: IMSLP loves, loves, loves PDFs and will not accept any other file types for sheet music. You are allowed to submit MIDIs of your own work, although it's not recommended. This website highly encourages that you submit recordings played by humans.
Style of composition: IMSLP is mainly a reservoir of classical and folk music, although it holds quite a few ragtime pieces, and jazz and gospel can probably hide pretty well in there. You might find a few examples of even more modern music in there if you search hard enough!
Publication criteria: The most important criterion for submitting music to IMSLP is this: It must be in the public domain or have a Creative Commons license. This means that you've got to be willing to let people distribute your work without express permission. IMSLP recommends slapping on a Performance Restricted Attribution-NonCommercial-NoDerivs 3.0 license for one of the most restrictive licenses: others can freely print off your work for personal use and play it privately--heck, they can play it in venues where nobody earns a cent--but they can't make a CD with it and sell it, sneak it into a video game that costs money to purchase, or rearrange your piece and publish that rearrangement. If they dare do, you have the power to shut down that use. You can also publish under a variety of less restrictive licenses.
IMSLP also will not publish anything with copyrighted material. Want to sneak in a quote from Leroy Anderson's "Sleigh Ride"? You're not getting that piece with that quote published unless you also hand in written permission from Leroy Anderson's copyright holders to use that quote. And let's just say that getting that written permission is extra hard. IMSLP uses Canadian copyright rules, which are more lenient than American copyright rules, but they're still strict enough to prevent a ton of copyrighted material from getting past the radar.
Type of recording: Musescore forces you to submit their exclusive MSCZ files. This means all their default audio is computer-generated. These are displayed on the website as musical scores with audio playback. Users can download MSCZs, audio files, and PDFs from the website. You can sync your pieces to YouTube videos, but I've found that to be a messy and inaccurate process. You can also publish your Musescore pieces to YouTube. They'll only let you do that once per day unless you pay for Musescore Pro, though.
Style of composition: Pretty much anything for classical to folk to jazz to pop to EDM to heavy metal to atonal stuff to heavy metal remixes of classical music are allowed. Musescore is unable to use actual words in audio vocals, so be careful.
Publication criteria: The most important one: unless you pay for Musescore Pro, you can only publish 5 works per account. Musescore will hide your least recent works if you publish more than 5 on a single account. People sometimes dodge this by creating tens of dummy accounts and publishing 5 works each to them. There's also stuffing several pieces into the same work (web page/submission).
Musescore technically lets you slap "all rights reserved" on your music by default. In practice, other users are pretty free to plagiarize you and re-distribute your Musescore works without your consent. It's your job to hunt those copyright-infringing people down. Even if you put Creative Commons or public domain licenses on your works, people will still plagiarize them.
Be aware that copyright holders can get your works-that-contain-copyrighted-material removed from Musescore. You can file a counter-claim if you don't use copyrighted material or you truly believe your stuff falls under Fair Use. In practice, the only works I've heard of that got restored from copyright claims are those that got taken down for really silly reasons, such as sharing only titles with copyrighted works.
Type of recording: Newgrounds likes MP3s and WAV files. They want detail. They know that people listen to their music with headphones and speakers that extract all the high-quality goodness out of their sound files. Submitting MIDIs is discouraged. (MIDIs sorta sound bad, anyway.) With that being said, you can freely submit computer-generated or human-generated music.
Style of composition: Again, pretty much anything for classical to folk to jazz to pop to EDM to heavy metal to atonal stuff to heavy metal remixes of classical music are allowed. Atonal stuff is probably not that popular, though.
Publication criteria: In general, follow https://www.newgrounds.com/wiki/help-information/terms-of-use/audio-guidelines. You can't publish anything with any sample of copyrighted music. You can't publish anything with stock loops. Publishing a rearrangement of a copyrighted work is risky, but I've heard several remixes of copyrighted video game themes on Newgrounds. Be aware that copyright holders can get such rearrangements removed from Newgrounds, though.
Also safely assume that Newgrounds publishes your music with the Attribution-Noncommercial-Share Alike 3.0 license unless you twiddle the license. Yeah, that means a lot of people can rearrange your music for free and distribute that. But hey, at least they can't sneak it into a movie without negotiating with you first!
Bonus impact factor: Newgrounds acknowledges that there's this killer popular mobile app out there called Geometry Dash that lets people create rhythm game levels with your music in it. If your piece is used in a particularly popular level, masses of people may love your work...for all the possibly wrong reasons.
Type of recording: Soundcloud accepts only audio files. They don't care whether humans, computers, or elephants generated the audio, though. They also don't even care whether you submit music.
Style of composition: Again, they don't even technically care whether you submit music, but anything from classical to folk to jazz to pop to EDM to heavy metal to atonal stuff to heavy metal remixes of classical music are allowed. Hour-long podcasts are also accepted. So are whale noises.
Publication criteria: Though stuff may sneak past the radar, Soundcloud declares that publishing works with copyrighted material is not allowed. Repeatedly doing so will get your account banned and removed from the website. ...And the copyright holders will be after you hard.
Type of recording: YouTube obviously accepts only videos. There are services such as TunesToTube that let you turn MP3s (and possibly other audio files) into YouTube videos. They don't care whether humans, computers, monkeys, or volcanoes generated the audio.
Style of composition: YouTube accepts any genre. YouTube also accepts non-music. Heck, it also accepts completely silent videos.
Publication criteria: The default YouTube license is technically fairly restrictive, which is decent if you don't like people re-distributing your work. However, people will grab your video and use it elsewhere in practice, so be vigilant. You can also publish your videos under more lenient Creative Commons licenses.
Be aware that YouTube will let copyright holders mute the audio or remove your video if you use copyrighted material (especially without their express permission). Upload too many videos with copyrighted material and YouTube may ban you and remove your account. (Get a loyal enough following, though, and other users may follow in your footsteps. See SilvaGunner for further information.)
In practice, your remixes of copyrighted works may never be removed, and you can get fairly famous posting remixes to YouTube. I'm a fan of listening to GaMetal, FamilyJules, DjtheSDotCom, and other people whose pretty much only YouTube publications are arrangements of existing copyrighted works.
Bonus impact factor: There is such a thing as YouTube monetization, where you get an AdSense account and let YouTube post ads prior to your videos. You can earn some cash this way, although from anecdotes I've heard, you're better off making a Patreon account and offering services to people who donate a buck per song if you want to earn money from your music. (They don't have to be much. Offering high-quality WAV files is fine at the $1-per-song level. Accepting commissions from these people is fine at the $20-per-song level.)