The Pi Needs 700mA simply to function. It needs additional power to operate basic USB devices such as a keyboard.
Initially, I bough a cheap 1000mA adapter for mine, but it was only just good enough to operate the device and a keyboard. If I tried to connect anything else, (like a flash drive) it would freeze or fail to boot altogether.
I’m now using a genuine Nokia 1.2mA charger and it does the job perfectly. I can power a cheap 4-port USB hub passive 2 USB Gamepads and a USB Keyboard without any issues. I could possibly have added a mouse as well, but I haven’t tried it yet.
As for memory cards, it doesn’t seem to matter whether you use a class 4 or a class 10. Performance is the same either way.