Infrequently. Last two playthroughs got wrecked by hyper-aggro AIs.
That is definitely a thing that happens. I'm not sure to what extent it's like Civ, but I do think that you have to keep your military beefed up to avoid some AI aggression. Others are just born that way (e.g. a fanatic purifier), and I've found diplomacy to be a much bigger necessity than in other 4x games.
I find that the hardest part is balancing expansion. In general, expansion is good, but there are some mechanics that make this require some pause. The more planets and systems you control, the longer it takes to get tech and unity perks. That said, as a general rule I err on the side of expanding, since eventually the map will fill up. Meanwhile, military expansion should be gradual but constant: you don't want to have to try coming from behind, and the stronger you are the less likely your neighbors are to mess with you.