How important could it really be? just asking the question means you're on the right track. While the quality water used and method of brewing are both important in determining how your coffee tastes, grinding, an oft-overlooked component plays a large role as well. If nothing more, here is a quick approach to the best ways to improve your experience:
Ok so we established that blade grinder aren't as good, they produce uneven coffee grounds and excess heat. Blade grinders, however, are the most common and If you find that is what you have available try to use it immediately before the water is poured and grind in short pulses to prevent heat build up.
To add another level of confusion there are conical vs flat burr grinders. Conical burr grinders produce better results due to less heat production during grinding. This is the point where you decide how much of an investment to spend on achieving the perfect cup and how it fits into your budget. The Baratza Virtuoso is generally considered a step up from the previously mentioned grinder but both will do a great job and are plenty enough for any home setup.
Please don't, convenience aside there's a monumental drop off in quality. Coffee is broken down by air, heat, and moisture and ground coffees expire in about 20 minutes. Investing in a grinder will be the most expensive part of your coffee brewing kit but also may be the missing component to achieving the perfect cup.
If we could make one thing stick it would be this, don't buy pre-ground coffee, any grinding method will provide a better taste and quality to the cups of coffee you brew.