switch mode power supply - Choosing resistor values to operate a Half Bridge Driver

I am designing a 10W (18-12V) synchronized buck converter with a Half Bridge Driver and 2 MOSFETs as shown below. The Driver get a PWM signal from a programmed micro-controller (a 15KHz, 3.5V pulse at HIN and LIN). The Driver IC is the IRS2003(S)PbF. After the inductor there is a capacitor (not shown here). I feel confident about these values. However, for the MOSFET driver, I can't see from the datasheet any instructions on choosing the resistors' values. I know I must protect the IC which has a maximum Output current of 290mA for the high side driver (HO I think). The MOSFETS used are the IRL60B216. The MOSFET datasheet shows that the gate resistance is 2 ohms. How do I determine the resistors' values? where do I look at within the datasheets?

Update:I tried this out. As in the answer below: "When designing a mosfet driver the important thing is ensuring those capacitors are charged and discharged quickly while not overly stressing whatever is driving them. The IRS2003 has a minimum dead time of 400ns and so you need then to switch well within that number." I got this waveform for the Vgs of the MOSFETs, the upper one is for the higher side.

I got this waveform for the dead time

which I'm assuming is wrong because the charging and discharging of the equivalent MOSFET's "capacitors" are taking more than 400nS. I'm staring the 18V input a 0V and increment it by .1V, which is causing a short circuit as I exceed the current rating of the power supply after 2V. What can I do to prevent this? I tried 10 ohm resistors and it improved the dead time a little. but I can't go below that I think.