I'm new to the DS scene too. I recently purchased an M3 adapter with a PassMe (Passme, SuperPass, PassKey, its all the same device packaged differently). It hasn't actually come yet, I bought it yesterday from Divineo, I decided to go for an M3 after about 2-3 weeks of researching stuff about the DS scene
All you really need is some kind of flash cart (Supercard, M3, EZFlash, F2A) thats compatable with the DS (From what I see most people go for the SuperCard or M3 and the M3, though more expensive, is hailed as a slightly better device) And for DS homebrew/roms ect. you need a PassMe/PassKey/SuperPass any of those.
Obviously you need a CF/SD card if you get an M3 or a SuperCard. If you get a normal GBA Flash cart keep in mind it's measured in Megabits so you need to divide by 8 to see how many megabytes youre actually getting.
Edit: I'm not sure if I actually answered your original question. A Flash Cart Kit would include a Flash Cart, a way to Xfer files from your PC to the flash cart such as a USB device, sometimes a PassMe... This is just coming from the Neo Flash kit. It's insanely overpriced and doesn't give you as much storage as M3 or SuperCard.
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