R4wood gave a detailed on how to choose a r4 card for your console at our old site, there recommends you on how to choose a ds gaming cartridge. While after the year 2017, we added more suggestions here according to our experience.
If you want cartridge to be used for ds games only, read the guide above at our old site.
If you want to play 3ds roms on consoles below, there are two options.
a) Do custom firmware (cfw) modification to your consoles
>> Flash boot9strap to consoles without cartridge/r4 card, do follow unofficial guide https://3ds.hacks.guide/, wrong operation may damage your console forever.
>> Flash boot9strap with help of cartridge/r4 card, there is detailed official guide on how to flash console, it is not very hard for tech newbie; Strictly follow the guide will not break your console but still with few risk.
>> Your local store may support this CFW flash service, you can ask for their help.
b) No need to modification to your consoles
>> Get a Sky3ds PLUS, you need to download clean 3DS roms, flashing into micro Sky3ds plus memory card directly to play, no need other setup but with region limit. This super chip is much expensive.
>> Old version blue Sky3DS, its setup is sensitive to your PC system, not recommended.
>> Stargate 3DS with CFW installation, compatible up to current 11.6 3ds system.
>> Gateway 3DS but with system limit to 9.2.