What is the ideal, healthiest relationship between a Platoon Leader and his/her NCOs?

This is an excellent question to see from a future 2LT.  I had a great relationship with my Platoon Sergeant, and we were friendly to some extent off duty, but it's important in my opinion that you never cross that line to where you are best friends, and the command relationship is blurred.  That goes both ways.  If you become too good of friends, or you go out partying all the time, it may compromise his ability to stay objective with his advice for you, and it may compromise your ability to maintain his/her respect on duty as the commander of the platoon.  Once you lose that legitimate respect, you may never be able to get it back. So, it's a fine line, but follow your instincts and build a strong relationship with your Senior NCOs and you'll do well with this issue.

Always show support for each other in front of your troops. If you disagree, take that discussion to another location, you don't want to undermine the authority of either of you by conterdicting the other in front of troops. Ask questions and offer advice. We Sr NCOs have a wealth of knowledge but we aren't the be all end all. If you don't know ask to find out, if you think you have a better way, discuss it and work together to find the final answer. The more your troops see you working as a team the more they will. You are the Sr person in the PLT. If you need to, stomp that foot down and hold your line. As CPT Kletzing has said, be friendly but mindful. Don't get so friendly that it becomes an hindrance to the stability and performance of your PLT. If you ask me Cadet CPL Nathman, simply asking this question shows a good bit about your desire to become a good and effective leader that can affect the unit you are assigned to. You'll be fine.