Low light fastest growing stem - dwarf hygrophila You could be cutting them and planting the stems once every week or two. Absolute best bang for the buck. I bought a bunch for $5 and got nine stems.
Floating - duckweed (as much as I didn't want it I got it for this purpose when adding a bunch of new fish) I understand that they are also great nitrate sinks too.
I went low light and tried 14 species of plants and those two are the best of the lot. If you want to see the whole list, it's in my aquarium tab in my name box (what's that called again?)
Quantity of plants to avoid the worst of a cycle, or to suck up the ammonia spike in a current cycle, would be 1 medium plant for every gallon of water and you could mix up faster growing with slower growing. Duckweed is so small that it would be a handful to a gallon... although I am not certain how they measure up in ammonia suckage.
Oh, I'll put a link in my signature to my shotgun approach I used in my planted tank.
I used about that quantity and put fish in (12 barbs) within a couple of days of filling and saw a very short nitrite spike about two weeks into the quiet cycle.