Some background: I picked up Dominion earlier this year. I really love the game and the expansions I have played. I wanted to get a second deck-building game, one with a fantasy theme and flavor.
After reading reviews on several different ones, I went with Ascension. My LGS didn't have the first set, Chronicle of the Godslayer, so I picked up Rise of Vigil. I really like the game. It is simple enough to play, but has the flavor I am looking for.
I am looking to expand beyond this set. Out of all the Ascension sets, which one should I get next? Should I pick up Chronicle next, or should I go with one of the other expansions?
I haven't really noticed any major changes in the game when adding expansions. You increase the card variety, so you're less likely to see some of the rare ones (but you'll see different rare cards) and fewer doubles of the more common cards (but lots of cards that fill similar roles).
If you play the game a lot, I'd recommend getting the expansions, just for more variety. If you don't play it a lot, they aren't really required.
There is also an itunes app for Ascension where you can play online with people or offline with the computer.
Another game to check out is Thunderstone. I found it interesting, but it took too long to set-up and put away for a card game IMO, it also feels a lot slower than Dominion and Ascension, but those are more my personal nitpicks than anything else. You send heroes into dungeons to fight monsters and can even level the heroes up (I think 3 tiers if memory serves).