To increase the collector current without saturating the transistor, us a lower value collector resistor. The circuit becomes saturated when the voltage across the collector resistor is approaching the battery voltage. If you have less resistance for the collector resistor it will have less voltage across it for the same current as a higher value resistor. The lower value resistor will take more current before its voltage approaches the battery voltage. The disadvantage of a lower-value collector resistor is it reduces the voltage gain of the amplifier.

Now for the gate resistor in the common-source amplifier.

The above circuit has no gate resistor. Recall that little or no current flows into or out of the gate of an FET. With no current flowing through the variable resistor there can be no voltage drop across it. The voltage on the right side of the variable resistor will be the same as the voltage on the left side. The gate voltage will be the battery voltage (V_GG) regardless of the setting of the variable resistor. Now look at the test circuit from Transistor Characteristics.

Here the gate resistor (R_G) forms a current path so current can flow through the variable resistor. It also forms a voltage divider with the variable resistor. Now, as you change the value of the variable resistor the gate voltage will change.

Also an FET will consist of either two conductive materials separated by an insulating material (for MOS transistors) or will be a reverse-biased PN junction (for J-FETs). Either way you have two conductors separated by an insulator—a capacitor (reverse-biased junctions in Semiconductors). So, an FET not only acts as described in these discussions, but acts as if there were a capacitor between the gate terminal and the actual gate of the transistor. The following illustration shows what an FET looks like to the rest of the circuit. The capacitor is actually part of the transistor but the circuit acts the same as if there were a capacitor in series with the gate.

An FET looks like a transistor with a capacitor in series with the gate.

In addition, these test circuits have a battery supplying the gate voltage. The output impedance of a battery is very low and will discharge the gate. In fact, we just discussed that without the gate resistor the gate voltage will equal the battery voltage. A real-world circuit will not have this battery. It will be connected to the output of another circuit or device. If that circuit or device has a high output impedance this "parasitic" capacitor will not be able to discharge when the driving circuit's voltage drops. (see Interaction of Output Impedance and Input Impedance and Capacitors in DC Circuits). As a result the FET gate will charge up to the highest DC voltage applied to it and sit there. The gate resistor (R_G) provides a current path to discharge the gate allowing the voltage to change. You will see this resistor in circuits where the output of a high impedance device or circuit is coupled to an FET.