It is true that, in most conductors, the actual charge carriers are negatively charged electrons, which leave the negative terminal of the power source, pass through the circuit, and return to the positive terminal of the source.
However, early scientists studying electricity didn't know about electrons, so arbitrarily declared that current flowed from the positive terminal of the battery, through the circuit, reeturing to the negative terminal of the battery. Today, almost everyone uses this "conventional" (positive charge) current, and you will avoid confusion by using it also.
Circuits work equally well whether you wish to think of them using conventional (positive) or electron (negative) current.
For your LED and resistor circuit, it doesn't matter which component is connected to the positive terminal of the battery, as Kirchoff's Current Law says that the current is the same at all points in a series circuit. That is, the resistor will limit current through the LED, whether it is placed "before" or "after" the LED, regardless of which way you think the current is flowing.