Bog should aim to be 30% of pond volume, you don’t want to get the pond very clean. Ie you don’t want to scrub off the biofilm on the liner or anything under water for that matter, you are just unnecessarily starting the pond from square one again. Just get all the silt and sludge off the bottom, plant mulm/debris out and will be good to go.
As for plants, most use a variety but there are usually a couple staples like water cress, forgetmenots, creeping Jenny that grow like wildfire and are the most effective at pulling out nutrients, but are easy to weed out as they take over. Also, use irises but be careful some put out an extensive root system, elephant ears, cannas, for some height variety and flowers really any marginal plants will work, even ferns and hostas will work in the bog.