I think with a yeast starter most people stir it for ~12-18 hrs then stick it in the fridge for a day or two. That way you can dump off most of the starter "beer", give it a swirl and pitch it.
With a lacto starter I'm not sure if decanting is better or not, but personally I do not decant. It is my understanding however that O2 slows down that culture so you may want to take it of the stir plate regardless.
I just keep my lacto starters in a mason jar inside a (blue!) cooler with a Ranco probe and heat pad at ~90* for about a week.