In the time we have together, let us drink often and well. What should we drink? Only that from which we take pleasure. The aim is not to change your mind about things you already enjoy--there is comfort and value in ritual, in the familiar. I offer instead to share my experiences in drinking and my understanding of why I appreciate what I do. Nothing that follows is meant as boast or brag. My knowledge is a small thing. I offer it up still, in hopes that when next we meet and raise a glass, we are all made happier by what we find in it.
Have you ever eaten wild boar salumi? Earth and mushroom, blood and iron, animal funk. Now imagine drinking and smelling those same flavors and you'll have some sense of the 1967 Oddero Barolo. This is why sensation junkies like myself love "mature" (or old) wine. They offer flavors and aromas that aren't present in younger wine. If drinking sausage lacks a certain appeal for you, I quite understand. In fact, it's better for your budget--wines like these often aren't cheap. But if you're intrigued I advise you to get yourself to a retail wine shop. Tell the staff you'd like to try a wine that has some age on it and be prepared to lay out a bit more money than for your usual bottle. When you get that bottle home, give it your full attention. Often you'll see the wine evolve in your glass over time (usually for the better, but not always.) Is the aroma wafting from the glass so tantalizing that you just want to breathe it in awhile? Does the wine coat your entire mouth? Do you experience a wealth of flavors in every sip, while still sensing a cohesive whole? If the answer to all of that is yes, you've got yourself a great bottle of wine.
You say you've never been much of a wine drinker or you're just starting out? I'd say start in the same place--get to a great wine shop near you. Once you're there, find someone on the staff that you feel comfortable talking with. Let them know your budget and let them pick some bottles for you. Once you've decided that you love wine you're ready to see if something like an older Barolo is worth your time and money. Again, mature wine offers mature and complex flavors and aromas. This does not mean that these wines are inherently better than younger wines. You owe it to yourself to try both.