Here's how I'd rank the sets:
1. Intrigue - works really nicely with the base set, doesn't increase the power level all that much, adds a lot of strategic space due to the theme of choices, without being overcomplicated. Probably my favorite set overall, plus hey, extra coppers and stuff. Although be warned, there are a lot of potential "now I hate Dominion forever" cards in this set: Torturer, Saboteur, even Masquerade has led to physical violence.
2. Prosperity - considered by many of my friends to have a substantially higher power level. As one person put it, "Prosperity is my favorite set because playing with Prosperity cards makes me feel like a badass." Higher power levels often translate to more fun games for many people. Whee, 100 point games!
3. Seaside - Mechanically, I'd put this one above Prosperity, just for having Durations, which are a great mechanic and better than VP chips, which are unique to Prosperity. But I think the overall fun factor is slightly higher in Prosperity -- there are way more killer decks you can build with stuff like Goons, City, Grand Market, King's Court, etc.
4. Cornucopia - Subtly powerful cards, but no unique mechanics, and it's a smaller set.
5. Hinterlands - More complex in its interactions than the others. Don't get me wrong, I like this set a lot, but if you only have base, this isn't the first set I'd recommend.
6. Alchemy - A lot of very powerful cards, but also a bunch of cards that are tedious and annoying to play IRL (Possession, Golem), and some people just don't like the addition of Potions. Plus, smaller set.