I've noticed some seafood restaurants put so much stuff on baked oysters, it completely overpowers the oyster. You could have baked a napkin, and it would have tasted just as good.
And then it can go the other way with raw oysters. I never understood the oysters when it doesn't taste like much at all.
An oyster has three key components that you want to be aware of when accenting their flavor: salinity, texture, and finish.
Oysters are naturally salty since their blood is basically seawater. Depending on where the oysters are from they can vary rather significantly in salinity, from 12 to 36 parts per thousand. Oysters from northern colder waters are typically saltier and crunchier than those from warmer waters. Acid is a natural counter to salt which is why lemon juice or mignonette are common flavorings for an oyster. If you're eating an oyster that is saltier than what you're used to an addition of an acid can help mellow out the punch of salt.
The texture of an oyster is my favorite part. The only way to eat an oyster is raw in my opinion. Baking just doesn't do it justice. There's something sublime about the feel of an oyster on your tongue and that burst of flavor and sweetness you get when you begin to chew.
The finish is the hardest part to discern. Detecting, and accurately describing the finish of an oyster is much akin to describing the flavor of a wine. Cucumber is often used to describe the finish, as well as melony, or even just fruity. If you drown your oyster in too much of any flavor you will miss out on this completely. How do you enjoy this and learn to detect it? I suggest tasting different varieties side by side. My favorites are Blue Points, Apalachicola, and Malpeque's. See what's available in your area from a good fishmonger. Try to get some from the Atlantic if you can and compare them to Pacific oysters. There's a very noticeable difference there.
In summary, let your oysters speak for themselves. They do have a taste that is completely unique, but you have to respect it and not mask it. Stick to the classics for flavoring: tabasco, lemon juice, horseradish, and mignonette. Venture out and try others if you want, but avoid sweet or salty additions, the oysters take care of that themselves. Acid and/or heat are what you want to add to accentuate the flavor of an oyster.
I recently had some at a winery restaurant where they were topped with a tiny bit of icewine jelly. That worked extraordinarily well - subtle enough to still get the full oyster flavour, but the sweet aftertaste of the icewine also provided enough contrast with the salinity to make it interesting.
There's a theory of cooking that argues that you should pair elements with chemicals in common. The FoodPairing web site recommends some "interesting" combinations with oysters:
I'm skeptical, but if anyone has any luck pairing these with oysters, please comment!
Your best bet is to look at the dominant flavour notes of the oyster in question--different species have different flavours. (We recently had at the restaurant some wild oysters from County Clare, Ireland, which had dominant flavours of melon and cut grass. Paired with a yuzu mignonette they were absolutely dynamite).
Anyway. Look at the dominant notes, and think about what pairs nicely with those. If you get oysters with a big cucumber flavour, mint could be absolutely gorgeous, when used fresh and with restraint.