Some things I want to add.
Generally speaking, if your pc is... quite old or not very good, tinker around with the cpu clock multiplier, most of them can run the emulator on 48 or 32 in my case, makes the game just work better overall. If your pc for any reason cannot handle a multiplier of 24, I would recommend switching to ANEX 86. That emulator is known for having good and stable framerate but, sadly, horrible audio and graphical quality. In the case of touhou, some bullets flash/blink and its really annoying.
If you are using neko project without Retroarch, you can setup a option for savestates in the emulator by heading to np21Int.ini and typing "statsave=true" in a new line somewhere.
Another option for an emulator if Nekoproject doesn't run would be T98-Next. Runs the first 3 touhous pretty decently in my really old laptop where Nekoproject couldn't. Don't expect much from LLS or MS though, you need a decent system for those.
