I don't think you need a driver IC...just use PMOS for the high-side and NMOS for the low-side. The gate driver is normally for really huge power applications where NMOS is used everywhere and because of the way NMOS switches on and off, you often need a voltage to switch the high-side transistors that is higher than what you can normally provide.
MOSFETs have 3 terminals. Gate (G), Source(S), and Drain(D). A small gate voltage controls the large current flow between source-drain. For NMOS, D is more positive than S. For PMOS, S is more positive than D. For NMOS and PMOS f the voltage at make the voltage at G as close to S as possible to turn it off. To turn it on, make sure the voltage between G and S are high enough.
Now go Google for H-bridges to read more. Come back with a schematic and specific questions and we'll answer them for you.