Through the years I have experimented with several different methods to keep the ingredients submerged.(glass disks. glass beads in a baggie, a sanitized rock etc).
But I have always returned to what my grandma did, (and she always had something fermenting in the root cellar.)
In her open crocks she used a inverted dinner plate with a jar of water on top (like SL suggested).
When fermenting in a jar, she would put a couple cabbage leaves on top to keep the ingredients in the brine.
I ferment in jars (4 different sizes)...and I use the cabbage leaves all the time.....works like a charm when fitted snugly inside the jar..
The outer leaves with the stiff broad stem that grow close to the core work best.
When the fermentation is complete, just remove the cabbage leaves, discard and add additional mild brine solution if needed.
Cabbage is cheap, readily available, and the leaves also have an abundance of the lactic acid bacteria needed to get the whole process underway.
Note: a plastic condiment cup(inverted) will help keep the leaves from "pushing up" too far and liquid from fouling the air lock.if you use one.
For "starters" ...when I decide to use one because of the combination or kind of vegetable, I normally use whey harvested from yogurt, but granted, whey does contribute to a distinctive flavor, aroma and some increased sourness.
When those attributes are undesirable (like when I'm fermenting fruits, carrots, garlic,greenbeans) I use Caldwell's starter culture, which has the live lactic acid bacteria. It's a little pricey, but I have never...not a single time...had a problem with a ferment with Caldwells. And if I'm fermenting a couple gallons of ingredients, its an expense I can justify.
That being said....if all I'm fermenting is a simple Kimchi or sauerkraut recipe, I never use a starter....just salt, and I can't recall the last time I had one fail....its been decades at least.
CM