Heather Telford( her blog is Bits and Pieces HERE
does fabulous sponging and told us she uses SU round sponges cut into four pieces. I tried gobs of different sponges before learning from her and finally achieving success. I battled the Tim Holtz applicators to get sponging without lines and finally gave up.
Breaking in a new sponge goes with the territory, so to speak, and maybe is more important than the kind of sponge. I have a blank piece of copy paper under the cardstock I'll be sponging and before I touch that cardstock with the sponge I sponge the copy paper in a circular motion until the sponging is smooth, THEN I touch the cardstock very lightly at first, so if there's any line or marking from the sponge I can cover it with additional ink. The harder you press, the more ink comes out of the sponge, so I start with a very light touch and am careful with the pressure, always opting for keeping it too light rather than too heavy.
EVERY time I put new ink on that sponge, I first sponge the copy paper until the sponge marks don't show and THEN I move on to the cardstock. I wasted way too much time and cardstock while learning and was helped by one of the Moderators here who posted that I should stop trying to use the TH Applicators I was having trouble with and try just using sponges.
By the way, Heather has You Tube video tutorials as well as her written instructions as she writes the information on her postings HERE
Practice, practice,practice and you will be making great sponged cards soon!