Question: I am new to being a DM and am pretty much learning as I go. I am curious as to what some of the more battle-hardened DMs on this site would consider the optimal Player Character versus DM controlled monster would be? Thanks for any and all suggestions.

Answer: 
Variety. Sometimes you want an even number of combatants. Sometimes the PCs should be overwhelmed. Sometimes the PCs should overwhelm. It's impossible to arrive at an ideal number, because when you use a number of enemies in a fight, that number becomes less interesting in the next fight.
I agree with valadil about the variety. It can be fun to fight waves of minions sometimes and one powerful solo monster other times. You should keep the experience quota system in mind for deciding difficulty as well. 

I used this [Encounter Calculator](http://kassoon.com/dnd/encounter-builder/) for a recent campaign and it was pretty handy for quickly tweaking the number of monsters to get to the desired difficulty level.