For vlotage smaller than 100V, MOSFET are the first choise; they have small Rds(on) and a ultra fast intrinsic reverse diode, so they r low cost.
for high voltages like 300V and upper, IGBTs are the best choise for their small voltage drop, but they have not intrinsic diode so manufacturers co-pakage an ultra fast diode with them, reverse diode of mosfets in this range of voltage normally have a bad charactristic, like large Trr and low dv/dt which make them a bad option for inverters and motor drivers.
about the drivers: today the best solution for mosft/igbt driver is HVIC driver, they r integrated drivers capable to drive/protect several mosfet/igbt.
for your application u can use one of HIP408X driver from intersil.
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I think HIP4082 is the best option for your application.
about the HEXFET:
HEXFET is the trademark of International Rectifier for their mosfet, this name was chosen because the top view of the mosfet consist of a large number hexagonal cell.
other manufacturer have their own trade marks like mospower from siliconix, and TMOS from motorola (NOW onsemiconductor).
though they name their product , they are Double Diffusion MOSFET (DDMOSFET) or Vertical MOSFET (VMOSFET) based on IR's HEXFET Technology.
BEST !