What should I consider when choosing a flash for a Sony A580?

Probably the first important decision is whether you need the convenience (and working speed) of TTL metering with a flash, or are you going to set up your shots in a more crafty way and so a (significantly cheaper) manual flash would suffice.

You can probably get away with a manual one for portraits and group shots (actually, it would be better to have at least two, so you'd have a key light for lighting the scene and a fill light to reduce shadows from the other side). Opportunities for candid shots, however, may come unplanned, and TTL would be of great help for making sure the flash gives the right amount of pop in hurry. Perhaps one TTL flash and one manual flash to help in off-camera work would be a good starting setup for you.

Note that Sony/Minolta hot-shoes are different from ISO 518 standard hot shoe that the rest of manufacturers use, so you'll need an adapter for most manual flashes if you want to use them on-camera.

Further factors to consider, no matter if you want the TTL or not, are still the same as when choosing a manual flash.

You'll probably also need some accessories for your flash - see "What's a decent lighting kit for getting started with portraits?".