This guide is geared toward the Neko Project II system of emulators. If you're using another emulator such as Anex86, you may find more useful information elsewhere. I am willing to eventually learn and write about Anex86, but for now I'm going to keep it to NP2.
To my recollection, NP2 doesn't often come with many of the necessary system files. The only exception appears to be NP2Kai, which is a fork made to function as a libretro core. This shouldn't be an issue for most games, but some older games that rely on BASIC may require them.
List of firmware for PC-9801 emulation:
BIOS.ROMFONT.ROM
FONT.BMPITF.ROMSOUND.ROMD8000.ROMOnly the BIOS and font roms are required, however the others are certainly good to have to ensure compatibility with everything. The last one listed, D8000.ROM, I have no idea what it does. I said it was required in my last version of this page, but I don't have it since moving computers and think it may be a NP2Kai thing.
There are a handful of sound files to keep around as well. Certain games use these files for drums, but for some reason other games have drums but don't use them(???) But if you want to play Touhou 1 with the full music, you'll need them.
2608_BD.WAV2608_HH.WAV2608_RIM.WAV2608_SD.WAV2608_TOM.WAV2608_TOP.WAVSince the PC-98 was a computer and not a console, its processing power changed over time, and some games may require more power than others. To access the settings for this, go to Emulate > Configure... and change the multiplier amount (value on the right) to something high. Touhou games will also require a lot of power due to the heavy amount of moving objects in the game, so definitely set it to something really high as a minimum.
While most games don't seem to give a shit, Touhou 3 in specific really cares about your GDC clock. Neko Project II by default has it set to 5MHz, but Touhou 3 wants it at 2.5MHz. To access the menu for this, hold END while resetting the emulator. You should get a menu that looks like this:
Press the down key to go to the second option, where you should see the GDC clock option at the very bottom. hit enter to access the menu, then go down to change the setting. You don't have to hit enter to finalize the change, but it won't hurt you if you do. While you're here, feel free to change the top option (which changes your terminal) to BASIC, to maintain compatibility with older games that need it.
Unfortunately, there's no quick and easy way to map numpad keys for Neko Project (except maybe in RetroArch.) If you're like me and don't have one at all, you can either use a numpad emulator like this one or bite the bullet and spend a few bucks on a cheap peripheral. You shouldn't run into too many issues, but the older the game, the more likely it only has numpad support.
To patch your games, software like Pachy98 and Delta Patcher are often required. You can also find a rompatcher online that can handle it for you, and I've personally had no negative results doing it this way. Checksums are to make sure that everything inside the files are the same (to minimize errors), but sometimes different checksums can be used and work alright. Just be careful!