Honestly, if you've got a 10g round cooler, I'd suggest just buying a kit such as this:
https://www.brewhardware.com/product_p/coolermashfb10.htm
brewhardware.com also has a ready to use 10g cooler mash tun.
the domed full false bottom and everything is set up and ready for you.
I'll Also suggest picking up the book "how to brew" by John Palmer. Or perhaps "homebrewing with beersmith" although I'm unsure if it goes over mash tun design (I don't have it)
John Palmer does go over lautering and mashing in his book pretty well I think, including some discussion as to how and why wort often channels.
P.S. I had responded to your other post on getting a bigger setup. Something of note, I use 32G SSbrewtech kettles converted to mash tuns with a false bottom and manometer, I have found that you CANNOT use a rig of this size to brew small batches of beer. You really need an appropriate grain bed depth scaled for the size of brew you plan on doing. This article covers some interesting information on Lautering and I found it to be helpful in understanding some of the issues I was having lautering deep beds and shallow bed. http://brewlikeapro.net/lautering.html
Cheers, and good luck!