I've been doing lots of research into PS1 audio for a while now and as such I know how difficult it can be to find good resources on the topic. There aren't any easy to follow guides out there (and it'll be a while longer until I'm at the point where I can make and release my own), so I thought I'd offer you a hub to share resources and questions regarding the PS1 sound system. I'm still far from an expert, of course, but I'll do my best. I've tried to give a few rough pointers below but for in depth info it'd be best to check out the sources or to let me know if you have any specific questions.

"The PS1 sound"
One question that came to me while writing this thread was "what's the trademark PS1 sound". Since the technical limitations started too loosen quite a bit more, that's a hard question to answer.
One option to get a PS1 sound would be using late 80s/90s synths presets. Composers seem to have used them to some degree. Check out this presentation of the Roland D-05 (a recreation of the Roland D-50 from the late 80s). Many presets definitely sound like something from a PS1 game in my opinion. Someone did mention, that the same also applies to Sega CD and Sega Saturn, though, so there's that. 

Someone also mentioned to me that they connect the PS1's built in reverb to the classic PS1 sound. If you want give that a try you can check out the no frills reverb plugin: 
https://github.com/BodbDearg/PlayStation1Vsts/releases

Resources
The three Net Yaroze (PS1 dev console) documentations are of course a really good official source for info on the console.  The Library Reference and Startup Guide might not be too useful unless you want to make a homebrew PS1 game that's supposed to run on an actual PS1 system. The User Guide should help you out a lot, not just in regards to audio but also all things PS1.

One could split the PS1's audio output types into two categories: streaming audio and "MIDI". 

Because of the switch from cartridges to CD, developers had a lot more space to work with. And as such they could now more freely add streaming audio to their game. There were multiple types of streaming audio that were used: Redbook Audio, XA-ADPCM and PS1-ADPCM (there are also many alternative names for the last one like SPU-ADPCM, Sony-ADPCM and VAG-ADPCM). While Redbook Audio was uncompressed (and therefore higher in quality) and larger in size, ADPCM took up only a fourth of the size. XA-ADPCM, as opposed to PS1-ADPCM, was not sent to the 512kB big SPU-RAM (Sound Processing Unit RAM).

Like I mentioned, the PS1 also supported "MIDI". I wrote MIDI in quotation marks since technically the file format was SEQ, which was almost the same as MIDI, though. If you've looked through the Net Yaroze Guide already, then you might've seen them mention that the devs got a MIDI (SMF, Standard MIDI File) to SEQ converter with their developer console. The MIDI system usually consisted of three file types: SEQ, VAG and VAB. SEQs were pretty much just converted MIDIs while VAGs were instrument samples (short instrument recordings/syntheses) and VABs sound banks holding the instrument samples. I'm not aware of any preset sound banks that came with the system, meaning that there aren't necessarily any trademark instrument sounds that apply to all PS1 games. Note that skilled peeps did some great things using the PS1s "MIDI" system, making the tracks sound really non-MIDI. See Legend of Mana for example (they also had multiple people manning audio positions that weren't really that common for other PS1 games such as Sound Manipulator, Sound Programmer, Sound Engineer and Sound Editor and Square also usually used their own SEQ drivers, giving them more options on how to manipulate the sounds).

A portion of the below sources are really technically oriented and may cause headaches (they at least did in my case), be warned.

Let me know if you have any resources that should be added or if you have any specific questions that aren't answered in these resources!