A large percentage of coffee from the supermarket is meh. I would go as far as to say that most of it is out of date, despite what the "best by" date says. It might be something you can enjoy/tolerate once you develop a taste for coffee.
Try finding a local coffee trader. These are usually going to be mom n' pop organizations. We have a fantastic trader here in Austin:
Texas Coffee Traders. You can chat with the friendly staff who are more than willing to discuss just about everything coffee related. They will give you tips on brewing etc.
Without getting too technical:
Beans should come from properly ripened berries. A lot of the mass produced brands usually contain beans from unevenly ripened stock. This gives you an uneven flavor.
It's best to buy coffee beans whole, but if you don't have a grinder that isn't an option (I don't). For the freshest taste, buy coffee that has been rosted within the last 3 to 5 days. The bitter taste usually comes from coffee that has been stored too long. A properly brewed fresh roast should provide you with a refreshing beverage that shouldn't need to be loaded down with cream and sugar.
The same kind of bean can be roasted several different ways. Make sure to try light and dark rosts. Dark roasts generally contain more caffeine, but light roasts are usually more acidic. I usually stick with dark rosts because the decreased acidity is easier on my stomach and I find them to be a smoother beverage overall.
I recommend using a stainless steel filter for brewing if you are using a drip coffee maker. It will bring out more of the flavor. A paper filter is going to absorb some of the oil during the brew and can take away from the flavor. Though paper filters can sometimes assist in removing some of the harshness of lower quality coffees. The best brew is going to come from a french press, but there is a slight learning curve to get a good brew and they aren't for everyone.
I hope some of that helps.