Connecting jumper to input pin
You need something to pull the voltage down to GND when the jumper is removed. A pull down resistor, as in your second example, is the usual way. Some microcontrollers have a built-in pull-down resistor, but it consumes more power because it requires a FET to switch it in.

Your second example with the resistor is probably the best option, and the only one that will work unless your micro has built in pull-down resistors. Basically zero current will flow through it when the jumper is removed, and only (10*Vcc) microampres when it is fitted.