Something to keep in mind is that good tea is more about subtlety and complexity than a real strong flavor. While some oolong can be flavorful, oolong is better known for being mellow and smooth. It will have more flavor than a green or white tea, but it won't be strong and brisk like a black tea. The more you pay attention to the nuances in the aroma, flavor, and aftertaste, the more enjoyable it becomes (which is something that continues on as long as you drink tea, not just when you're new to it).
Also keep in mind that you're going to get what you pay for - there are very few Tie Guan Yin's that I like, and I don't think I've encountered a cheap one that I would actually buy. I hate to say it, but I've also never been particularly impressed with Adagio's offerings oolongs. I know some people here are fond of them, but I think you can do better.
The best thing to do, for sure, is to try to find some good tea shops locally (preferably run by and for your local Chinese population) that will brew some samples up for you. You can pick some out visually (like some jade and roasted oolongs) and try them to get an idea of what you generally like, then buy something you like and try it on your own. One nice thing about oolong is that you can often get many infusions, so even though you may be getting a lower quantity than you were originally looking for (maybe you'd end up with 50g for $15 instead of 100g), you'd be getting a lot more infusions than you would with a black tea, for example. This is especially true with the Taiwanese oolongs, which can seem very expensive until you realize that 5g of leaf can give you 5-10 cups instead of the 1 or 2 you'd get with a black tea. The higher the quality, the more infusions you're likely to get.
With all that said, TeaCuppa is a great place to start for buying online. They are in Malaysia, but shipping is pretty fast and quite reasonable and their main specialty is oolong (although they have great greens and blacks, too). Whenever I've used their FedEx shipping ($14 USD) it's always arrived 2nd day. If you don't mind waiting you can get their standard shipping for $4.
Here's some good starters from TeaCuppa:
(from Wuyi mountain) - Thick and sweet with a light and floral taste and aroma. It's not complex, but it's a very satisfying tea that's also very
inexpensive and made to brew in larger quantities (ie, western style). This one also tends to yield a good number of infusions.
Magnolia Dan Cong
- Well defined fruity and floral flavor. Dancong is typified by the taste of peaches and oranges and some have hints of flowers as well. The taste and aroma are very prominent without being overpowering like flavored/scented teas. I don't recall how well this one holds up (I only got a sample and it was about a year ago), but Dancong in general will often yield many infusions.
http://www.teacuppa.com/Magnolia-Dan-Co ... ng-Tea.asp
- Fairly robust flavor with a mellow character. This is the most common of the Wuyi teas, and probably the most boring of them (Wuyi rock teas are renowned for depth and complexity when you know how to brew them), but it's probably one of the best to start with. This Shui Xian also opens up a bit and reveals more depth when you get it brewed right, which is another thing that makes it a good one to start with particularly if you're interested in getting serious about tea (such as gongfu brewing).
Lao Cong Shui Xian
- (Lao Cong means "old bush") If you want a Shui Xian with a little more depth and interesting flavor then Lao Cong is a good one that doesn't cost too much more. It's like Shui Xian, but it's more refined and has some deep fruity notes. This is one of my favorites overall.
http://www.teacuppa.com/Lao-Cong-Shui-X ... ng-Tea.asp
Bai Hao/Oriental Beauty
- This one generally appeals to those that really like black tea. It's a lot like a black tea but it's mellower/smoother and the fruity and floral aspects of the tea are exemplified a bit. It's kind of like taking the hidden qualities of a black tea and bringing them out where they become more obvious. On the other hand, those that aren't big on black tea often find Bai Hao pretty lackluster and generally unexciting. So get it if you're fond of black teas, but otherwise you might want to pass (or just get a sample).
TeaCuppa also sells samples of their teas for a few dollars, and usually includes one or two samples with every order. The free samples are smaller than the ones you buy, usually just enough for one pot, but at least you get to taste it. You can usually request that the sample be a particular tea if you want, otherwise they'll just try to include something that they think you'll like. You can also contact them for recommendations, they always seem to be happy to talk to customers about tea. (No, I'm not affiliate with them, in case you're wondering. They just became one of my favorite vendors, for a variety of reasons.)
I think it's great that you got gaiwans already
I think it's a lot easier to learn to use them well when you're just starting out with tea. They're not hard to use, by any means, but they can be intimidating to some when you've invested a lot of time trying to learn to brew things "right" western style and then see talk on the forums about very specific parameters by people trying to get things "just right." Doing gongfu, however, you get tea that is much more well-rounded, flavorful, and complex - things that otherwise get diluted out when brewing western style.