Of course, before we go diving into answering those questions for you - you have to know what kind of memory your camera takes! Luckliy this has gotten a LOT easier in the past few years as well!
First, a memory card is an electronic data storage device used for storing digital information. They are commonly used in many electronic devices, including digital cameras, mobile phones, laptop computers, MP3 players and video game consoles. They are small, re-recordable, and able to retain data without power. Remember your lens is the eye, the sensor is the brain and the memory card is the "mouth" of your digital camera. I like to think of the memory card as the mouth because its the first step in sharing your images.
Your camera manufacturer determines what type of memory they want to use for their devices. When digital first came out, each manufacturer (or most) had "their" own separate kind.. luckily now most opt for the very popular SD (secure digital) style. It basically won the war being small, and more durable then other competition.
Since point and shoot, bridge and DSLR's for the most part all use SD style cards I am going to focus on that for the rest of the post, however do take a moment and check your camera though. If you have a CF (compact flash) or something else from an older camera - be sure to check with me for some extra safety and purchasing tips!
Even within the SD card style there are differences... what you will first notice is SD and SDHC
SDHC - Secure Digital High Capacity memory cards are simply cards with a minimum capacity of 4GB (gigabytes). They are still the same physical size the SDHC Cards are newer and used for devices that require a higher capacity card. This also comes with a performance to match. SDHC cards are designed for devices that are compatible with the SD 2.00 specification. (faster)
Remember, if your device accepts SDHC cards, it is backwards compatible with standard Secure Digital (SD) cards.
SD Cards: Were the first style and slower with a 1.0 and 1.1 specification (if your into the numbers thing / for everyone else these are simply slightly slower for writting information and downloading it to your computer). If your camera says SD only for use you will not be able to utilize SDHC cards. To check if your device is compatible with SDHC look in your device manual or on the packaging, even the card door will typically have it written on it if it accepts the SDHC cards.
Now every card (regardless of style) also tells you the SIZE of memory within the card itself. Remember our chart?
Or a GIG (Gigabyte) like the chart shown above have....
and very quickly were finding TB (terabyte cards will be/are coming out into the marketplace... but we probably don't have to worry you about them right now... just know its like 1000Gig)
You need to know what these mean so you know what your purchasing... 32GB will hold 32 times the amount of information as a 1 GB card.... and depending on your MP(mega pixels) and sensor of your card... this will vary the amount of images you get on your memory card - right? Again, I am going to suggest you get at least 2 cards... and if you go on vacation or shoot a once in a lifetime event... use at least 2 cards swapping back and forth... you know... all your eggs in one basket and safety in numbers and all that... I like back ups :)
You also should be aware that there are different SPEED of cards. This determines how quickly it can accept new information from your sensor, and how quickly it will send the information to your computer. Kinda. You see, faster cards are better... unless your camera, or card reader, or computer, limits the cards speed. So you may or may not see the difference with a faster card. Technically the speed rating deals with some other things as well.. but overall this is the nitty-gritty of it. I would say if its not a price issue for you - get the higher speed card. When you upload as many images as I do .5 of a second here and there really does start to add up and my time is valuable.
Brands: Just like I suggest a good manufacture for your camera I suggest a well known one for your cards as well. People who have been in business longer and are well known usually stand behind their products and put out better products (in general). I know many photographers who will only shoot with Sandisk cards, and I know others who swear by Lexar. Personally, I have used both and they would top my list as reliable manufactures. They are not the only ones out there... but it would be my suggestion to stick with one of them.
Don't forget: Check your card packaging for warranty information or recovery software. More then once I have purchased Lexar cards that came with recovery software and have used it to recover images from friends cards. Funny enough never my own card, go figure. But good to have regardless!
Another thing you should know is that while the SD card is fairly durable, they can be damaged. They do get errors, corrupted files, and can even lose information or become unreadable. Hense, the tip about having some recover software! Anyways, I have found that these things are more likely to happen in high humidity areas, as well as if they are being handled in dry areas... static shock. Water Damage is also not good... so don't store them in your pockets or anything else that might go into the wash. Trust me.
I have found the best way to keep track of, and keep my cards safe is a memory card holder like this. I like the hard case designs, but have several of the cloth ones and they work well also. They hold the cards in place, and you can tuck one of those silicone packs that come with your shoes inside to keep moisture out. (great in your camera bag also) I even keep a cleaning cloth in mine so I can clean my lens when I change by card. Handy.