If I intend to play the fort for the long haul (which is usually the case), I will check for a couple of things in legends and the embark screen (making a backup save of the region beforehand or using the "die" function of DFhack) so I don't waste my time genning a site I don't want any business with.
1) Unusual nobles from Legends (Goblin King, Vampire Queen, etc...)
2) The civilization have the forms of clothing I want from the embark screen, since its possible for civilizations to be able to produce a certain type of clothing but not other variants of the same type. e.g. low boots but not high boots, vests but not tunics or shirts.
3) Access to colored stone, ores and minerals I lack at my site and would like to have from the embark screen. (I like to color code my levers, and embarking with bauxite and olivine right from the get go is pretty nice.) You can always purchase more from the dwarf caravans later.
4) Names and number of Gods and the spheres they govern from Legends. Generally, the more variety and less overlapping spheres the better for me, though I have been known to pick civilizations with a smaller pantheon but has a god in it with a name I really like, like Monom Fancyactions in my current fort.
Meh, most of these are just cosmetic differences anyway.
As far as I know, when it comes down to migrants its luck of the draw, but the civilization will try to send those dwarfs with professions that dwarfs in your fort do not yet have. (Thanks for the Legendary cheesemakers and beekeepers!) At least that was what I remembered was true for the previous version prior to 40.xx. I just roll with what I get and train those that I need from the more useless chaff.