My family and I decided to buy the expansions in the order they were released, hoping for a gradual increase in complexity. We bought Dominion: Intrigue and Dominion: Seaside, the first two expansions1. After playing with these, I have concluded that they are the best candidates for a new player's first expansion.
If you only plan to buy one expansion for now, you'll have to choose between the earlier release, Intrigue, or the more complex expansion, Seaside. I'll give you a comparison so you can choose wisely.
Intrigue2
Intrigue introduces kingdom cards that fit multiple categories. For example, the Harem is worth two treasure and two victory points. It counts as both a treasure card and a victory card.
Intrigue also allows you to play with more than four players -- if you want this, buy Intrigue first.
Overall, Intrigue is great for casual games with lots of players who want to screw with eachother using attack cards that may or may not be effective. The main weakness of Intrigue is that many of its cards are inconsistent, in my opinion. For example, the Tribute action card gives you a bonus depending on the top two cards of an opponent's deck -- who knows what you'll get? A lot of Intrigue cards are very situational or just plain weak4.
Seaside3
If you're ready for complex cards, Seaside is full of them, and most of them can be viable and consistent.
Seaside introduces duration cards, which are action cards that affect your next turn. A simple example would be Merchant Ship, which gives you two treasure on the turn that you play it, and gives you two treasure on your next turn as well.
Seaside also adds action cards that set aside cards in "mats" that are separate from your deck. For example, the Native Village stores the top card of your deck in your native village mat. Later, you may use a Native Village to instead draw all the cards that you've stored on the mat.
Dominion's designer, Donald Vaccarino, says that he did a better job with Seaside than Intrigue4, and I agree -- Seaside is better than Intrigue if you want to play strategic games with 2-4 players.
References...
1 n.a. (2012, Aug 7) Dominion Expansions. Retrieved from http://dominiongame.info/category/dominion-expansions/
2 Dominion: Intrigue Game Manual (2009) Dominion: Intrigue. Rio Grande Games, Rio Rancho, New Mexico.
3 Dominion: Seaside Game Manual (2009) Kingdom Card Description. Rio Grande Games, Rio Rancho, New Mexico.
4 Theory. (2012, Dec 21) Interview with Donald X. Vaccarino, Part II: Dominion. Retrived from http://dominionstrategy.com/2012/12/21/interview-with-donald-x-vaccarino-part-ii-dominion/