It's a little confusing, yes. Although it says Not Charging when you plug it into some USB ports, it should fill up when the iPad is sleeping.
Macworld Magazine wrote a great article about iPad power requirements:
It explains a lot.
The wall adapter is rated for 100 to 240 v (which I think covers every country), so you should just need an adapter for it and not a convertor.
A lot of computers (especially older ones) generally do not provide enough power to their USB ports to charge the iPad at a sufficient rate - it may still be charging slowly, and should be a bit quicker if the iPad's screen is off (if you leave it for a while and then disconnect it from your computer you may find that it's battery percentage has gone up). The wall charger is usually the most efficient way to charge the iPad.