If you're like me, you never owned a flash drive because you could upload everything to Gmail. You didn't worry about your memory card's size because you could just upload everything to your computer.
Mission life is a bit different. Here are some tips to avoid future, data-induced headaches.
Towards the beginning and middle of my mission, I thought, "You know, I'll just have smaller memory cards, then I'll have a flash drive where I can just move the pictures once it's full." However, for me (and missionaries who did the same), that proved time consuming and it ate up emailing time. It presented other problems. At an internet cafe (which is usually where you'll email), an elder I knew lost all of his mission pictures he saved on his flash drive because the computer had a virus. A sister I served with had some pictures saved on a flash drive, and they disappeared. I lost pictures I had copied from a companion (note: they were lost on my flash drive, she still had them on her memory card). Now, it could be that those pictures ended up in hidden folders, but you won't have time to look for them while you're emailing.
Other missionaries used memory cards and flash drives without incident. However, if you want to play it on the safe side, I recommend buying several high capacity memory cards before you leave on your mission. Once one is full, you won't have to worry about moving pictures off of it. They are cheaper in the US (example: an 8 GB memory card can cost under 10 US, but costs a standard 20 US on the islands). To give you an idea of how many gigabytes of pictures you might take: I probably took a medium-amount of pictures on my mission. I didn't take a lot towards the beginning (because I only had smaller memory cards), but I took more over time. Totaling it, I have about 24 GB worth of my own pictures, give or take.
Now, for flash drives! I think I mentioned before, but you may want to consider bringing a high capacity flash drive so you can copy your companion's photos. These are less expensive in the states (for example, a 16 GB flash drive can cost you under 20 US, while it costs about 37 US on the islands).
If you have to buy memory cards or a flash drives while serving, they have normal brands like HP, Kingston, and PNY, depending upon where you serve.
My last piece of advice: If you let a missionary besides your companion borrow your memory card, make sure you get it back, or that you know where they placed it. Slightly obvious, but this might also save you a lost memory card.