More than likely you’ll need to replace the stock bars to maximize the setup. But as a long-time former racer I urge you to take one step back and make sure you buy coil overs from a manufacturer that specializes in coilivers for your application and has proven race results to back it up. Not all coil overs are created equal.
If you buy coil overs from the right shop they will be able to advise you on the bars too.
Also note that, most likely, installing coil overs will move you to a more expensive class. Anything other than a “stock” class can get very expensive, very fast. The more mods that are allowed the more expensive it gets...