Q: Can I use emulator?
A: Yes. Note that the only allowed emulators for running are BizHawk with the mGBA core selected, or mGBA standalone, both along with the GBA BIOS.
Q: Can I use a flash cart?
A: The Minish Cap utilizes an EEPROM chip for saving the game. To put it simply, this takes time, around 5 seconds on average. Because the EEPROM chip is in the cartridge itself and not part of the game, it gets ignored in emulators (with the exception of mGBA) and flash carts that save the game by different means. This results into gains of several seconds and is more of a grey area when it comes to Minish Cap speedrunning. Due to this, the community has decided to place a ban on flash carts.
Q: What about 3DS, Wii U and Switch NSO?
A: Over 10 game saves, the 3DS Ambassador version saves the game around 5 seconds faster over a real cartridge, the Wii U VC version about 20 seconds, and the Switch version about 15s. As these options are "official" unlike flash carts, they are allowed for running. Really it's up to you if you decide to take advantage of save speed by playing on either console.
Q: What version can/should I run on?
A: The fastest version to run on is the Japanese version, followed by the European version and lastly the US version.
The EU version is the earliest and buggiest version of the game. Some might thus assume it's the fastest version to run on, though this isn't the case. Late in the game you have to fly out of the second to last dungeon, but for whatever reason, the European version lacks the ability to do so. This causes a loss of around 45 seconds compared to the Japanese version, not including the time lost from slower text which has yet to be measured.
Both the European and Japanese versions also have a trick called "Portal Items" which was patched in the US version. This trick is used to skip the boss key of the third dungeon, saving about 3 minutes over the US version.
It is also to be noted that the run employs a few RNG manipulations, which only work in the Japanese version. Due to this, running on anything but the Japanese version isn't recommended.
Q: What options do I have for capturing the game footage?
A:
PC Emulator: "Perfect" quality, costs nothing. Has potential input lag.
Real GBA + Webcam: Your choice.
Game Boy Player: The most costly part is the disc, assuming you already own a GameCube. The disc software gives decent quality, but consider the Game Boy Interface homebrew if you want something better. The GBI homebrew also works as an alternative to the disc, meaning you only need the GBP unit itself. Read here if you're interested.
DS Phat capture mod: Costs about 50 dollars for an installation, might not be easy to find. Great quality otherwise.
3DS capture mod: Costs around an eye-watering 250 dollars for an installation. By default, the game is scaled rather blurrily to fit the 3DS screen. If you hold Start or Select while booting the game up, it shows up in native resolution. This does result in a smaller screen though.
Wii U VC: Good quality, though the screen is a bit dark. You will need a Japanese console (or some modding) to run the Japanese version.
Switch NSO: Very high quality, colours can be a bit different to other versions. Very easy to play on JP, just create a Japanese nintendo account to sign in on, then download it from the store. Downside is you have to pay $35 for a year's access, or $10 for a year if you can join a family plan with 7 other people, ask in the discord if you are interested.