More national firms like Alston are going to give you more job security than the smaller firms. If they're listed in AmLaw, check their PPP (esp as compared to last year and the year before) to get some sense of how the firm is doing financially. Also, do a search on abovethelaw to see if there are any lay-off rumors or other red flags.
All that said, I wouldn't be too picky in this economy. If you get an offer, take it. You want an offer, you want to get your foot in the door, even if it isn't perfect right away, you have a better shot at moving around after your first year than at getting a job after graduation if you don't have an offer on the table at that point.
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