Since the invention of the SD card almost twenty years ago its specifications are laid down by the SD Association, group of major players for production of storage media. Kingston, Micron, SanDisk and Samsung for example are among them. If you've ever bought a SD card, you've likely come across these names. The SDA decided to categorize cards so that we can better distinguish between them and decide which card fits our needs. That was a pretty smart move. Unfortunately they didn't plan much ahead and whenever the circumstances shifted they came up with a new way to categorize cards. That was a slightly less smart move and resulted in card descriptions like
SanDisk Extreme PLUS 32 GB micro SDHC UHS Class10 U1 V10 A2
I made that one up, but such names are not uncommon. Even if you remove the the name of the company producing the card (in this case that would be SanDisk) and the name of its line (Extreme PLUS), there's still a lot of information left. I'll try to explain how they all effect us below.
This one's easy – that's the size of the card. How much space you want is pretty much up to you. A Retropie image is not that big. Unless you want to use your GBZ to watch videos, most of your space will probably be used by the games themselves.
So, how much is enough?
Well, most ROMs are small by today's standards. A complete collection of all NES ROMs is said to be just about 115MB. All SNES games come down to about 900MB. All N64 games make 4,5GB. The newer the games, the more space they need. But unless you aim for complete catalogues of the newer systems or a lot of MAME games you might not need very big cards. In most cases I'd say that 16 or 32GB are easily enough for the lifetime of your GBZ and then some.
That's the physical size of your card. SD cards come in three sizes: SD, miniSD and microSD. We need microSD, it is the only format the Pi can read without additional hardware.
This is the SDA's description for the size and the file system the card has to support. We have ordinary, high capacity and extra high capacity cards.
SD cards hold up to 2GB, support for FAT12/Fat16 is mandatory (4GB cards with this format exist, but are not guaranteed to work flawlessly as they operate outside the specifications).
SDHC cards hold between 2GB and 32GB, support for FAT32 is mandatory.
SDXC cards should hold between 32GB and 2TB (but smaller sizes exist) support for exFAT is mandatory.
I'd stay away from ordinary SD cards. They are not only small but also slow due to their age. If you get a 16GB/32GB card it doesn't really matter if you happen to stumble upon SDHC or SDXC hardware – Retropie converts the file system to ext4 anyways.
These are the SDA's categories for the speed categories for the cards. Yes, that's right – they have categories for categories. And they all overlap.
We have normal speed, high speed and several ultra high speed classes. My advice is: Do not make your decision which card to buy based on these categories. Practically all current cards that we might use fall in the UHS-I or UHS-II categories anyways.
The speed categories: C, U, V & A
This is where it gets really messy. We have speed classes, ultra high speed classes, video classes and application classes. Again, many of these overlap.
C2, C4, C6 & C10 are the speed classes. The number shows how many megabyte per second can be written to the card sequentially under the worst circumstances. So a C10 will always be able to write at least 10MB/s.
U1 & U3 are the ultra high speed classes. U1 is the same as C10 and guarantees 10 MB/s written. U3 guarantees 30MB/s.
V6, V10, V30, V60 & V90 are the video speed classes. They work exactly like the C classes, they are just named differently. So V10 is the same as C10 and U1, and V30 is the same as U3. Again, the number shows the minimum write speed.
A1 & A2 are the application speed classes. These guarantee possible operations per second and are useless to us.
You should look for C10/U1 or U3 cards. Faster cards quickly become very expensive.
Oh, and here is an overview from the SDA's site:
Sooo... where does that leave us?
If you have taken a look at YaYa's guide (and you really should!) on how to save your SD card most write cycles you might have noticed that all the speeds mentioned above are measured in write speed. That's because these cards are usually used for photography where write speed is the most important factor. A GBZ however doesn't have much data to write, we are looking for read speed. Faster reading means faster booting and faster loading. The difference between a fast and a slow card can easily be more than an ten second longer bootup of the system.
Unfortunately read speed isn't in the specifications. However cards labeled C10/U1/V10 often reach 50 MB/s and some U3/V30 cards read up to 90MB/s. These are what you should aim for. I've used SanDisk's Extreme PLUS line and Samsung's PRO Plus line. Both get high read speeds and both will set you back about 26€. If you want to go cheaper (and smaller), the SanDisk Ultra 16GB and the Samsung EVO 16GB are both about 12€, but don't reach quite as high read speeds. Still they are perfectly fine for the GBZ. There are of course a lot of other cards that are capable of that, too. But not all manage to read fast. When in doubt you should look for tests that include random read speeds.
Oh, I almost forgot: Don't buy your cards on ebay or aliexpress, where you cannot get hold of the seller. There is unfortunately a lot of fake cards on the market that have lower speeds and less GB than what their label says.
More detailed information on the topic can be found on Wikipedia and on the SDA's site.