You can capture as many units of a class as you want, but keep in mind that your prison has a limited number of spaces (which you clear up when recruiting units, obviously) and that you cant capture "invader" type enemies (aka purple invisible enemies), only human ones. Just keep in mind that most generics kinda suck, barring a few interesting enemies. Oh, and they can promote but not class change with a heart seal.
You get to pick 5 units (any unit, generic or unique) to put in your einherjar shop once you beat the game, and it carries over to other playthroughs via your unit logbook iirc.
there are also a few capturable bosses, mostly from children's paralouges. The full list is somewhere on the fates section serenes iirc.