Growing some of your own vegetables and herbs is a great way to introduce yourself to the flavors of food. While this will certainly elevate your dishes, don't forget to try each and every one of them plain. Try them uncooked, then cooked too.
You can also seek out either higher end grocery stores or ethnic grocery stores. You're not looking for high price...but you're looking for good ingredients. If you're going to buy something...see if they offer varying varieties of the same general item. I would forget about the blind (or double blind) tests right now. I don't think that you're testing your ability to distinguish one item from the next. You need to develop your preferences first.
My suggestion? Plant a garden, oh...I already mentioned that. My other suggestion...when you buy a plum...by one of each variety and taste them side by side. Same with eggplant, peaches, apples...do a side by side tasting. This is also great with meats. You really don't need a HUGE steak every single time you grill out. If you've got a store that sells prime beef near you get one prime steak and one regular choice steak. Cook them the same and lightly season. Try them side by side and see what you think. If the prime steak is too much money then next time your thinking of cooking steaks, just go without and save the money. If you pass on cooking the steaks a couple times in summer you'll have saved enough money to get the prime steak for a side by side comparison. True, many of us have had a prime steak before and it's easy to say that you preferred it over choice. But doing a side by side you get to directly compare all the nuances within the meat. The flavor, the fat, the mouth feel, the texture...etc.
Also...go buy something expensive. I absolutely love prosciutto, my favorite being Jamon Iberico Bellota. It's expensive...really expensive! $179.00/lb. But you know what...I buy only a couple of slices and that's it. It'll usually cost $7.00 to $14.00 for a couple slices, well worth it in my opinion. Plus you may get to know the person who does the ordering and get a wonderful Iberico Bellota end for a heavily discounted price
Don't pass up the chance to try new flavors...just adjust the quantity to fit your budget. You don't have to do this all the time...but every once and a while.
enjoy the food!