A powered hub should provide the USB standard power to each of its ports. That will be 500mA (for 2.5W per port) for USB 2.0, or 900mA (for 4.5W per port for USB 3.0). The rating of the hub should match the total power of the ports (the number of ports will drive the hub's power, so you can't go by just the total power figure).
Multiple thumb drives shouldn't have a power issue on a USB 2.0 hub, although the hub could be a bottleneck in terms of data bandwidth. That said, USB hubs have notoriously high failure rates, so that could be an explanation if you're having problems with thumb drives. If the hub's ports work fine with other devices, and the thumb drives work fine if you plug them directly into the computer's USB ports, then there's a different issue that should be the subject of another question.
Hard drives can be a different matter because they need more power. Small drives can often be powered by a single USB 2.0 port. Larger drives often need to be powered by a "Y" cable and two USB 2.0 ports (technically a violation of USB standards), or a USB 3.0 port.
But you also need to consider the USB class of what the hub is connected to. If the devices you're plugging into a USB 3.0 hub are USB 3.0, they can draw USB 3.0 power levels from the hub. If they are USB 2.0 devices, they might be limited to USB 2.0 power levels (a USB 2.0 device should never try to draw more power than that, regardless, although the rules are violated for drives or enclosures using a "Y" cable).