Receiver/Shank sizes

[ADQ K9]

My truck has a 2.5 inch receiver. Just ordered a new 2.5 inch shank for my WDH. I did not like the play with the insert on the 2 inch shank that came with the hitch. I figure I can use the insert for lighter stuff that I tow that requires a 2 inch shank. When it comes to the TT though I want as little play as possible. I figure now there is at least 1/4 inch of play both vertical and horizontal. What amount of play is acceptable when I get the 2.5 inch shank and How can I reduce the play?
On another note I hear the newer trucks are coming with a 3 inch receiver. I have never seen a hitch set up go into a 3 inch reciever unless it is on a Class 8 tractor with a 24 K pintle hook.