Yeesh. Stop saying "assault rifle". That term carries such negative baggage and has no real meaning. AR (automatic, not "assault") will serve you better
With a $2k budget, your options are WIDE open, recent scarcity notwithstanding. A 308 AR-10 would be super cool but that's a huge round, likely more than you need. Consider a Colt 6920 AR-15 instead. If you can find one, that is.
Is the zombie apocalypse scheduled for tomorrow? I thought it was end-of-the-year.