Your choices are autoloading rifles and, though both HK and Steyr are fine choices, they potential for affordable accessorization (should that be a consideration) is limited compared to the AR-15 variants, for which a great spectrum of aftermarket products are available.
If more precise shooting is also your intent, the autoloaders will provide very serviceable accuracy but I agree with the recommendation for a bolt action rifle for greater accuracy potential. The Remington Model 700 with the heavier "Varmint" contour is certainly an excellent choice, and there are others makes and models as well.
If you handload (or intend to) the .223 will provide you with more affordable practice and lower cost for components...more "bang for the buck".
You mention you intend to start hunting, but you didn't say whether your quarry is small game or medium game. That decision will affect others, as the .308 cartridge moves to the forefront of your two choices in either the autoloader or bolt action rifles.