There are probably a few points to be gained by having zeros on all your accounts, though reporting something ( allowing a statement to cut with a balance ) may eventually help your score also.
The problem with always having zeros on all accounts is, once one of those cards reports a balance, you will get a short term reduction in your FICO score because it is "taking on new debt". The score will recover as the calculation gets used to having a balance on that card.
If you are relatively new to the credit world, and (as it seems) you have no negatives in your file, then the best way to improve your score is just to not miss any payments. Month after month for years of No Missed Payments is the single most effective way to get the best score possible.
There's nothing wrong with paying as soon as charges are on your account, because you will never have a late payment in that case. As to building a comfort level with lenders that you are able to borrow money, to have balances on your account, and pay them off (PIF after the statement is fine), pre-paying everything may not help in that regard. Letting statements show balances of normal amounts of spend and paying those within terms, over the long run, can help with future apps with other CCC.
Just never miss a payment and the FICO score will take care of itself in a good way 
@Anonymous wrote:I always pay my credit card balance in full the day the charge posts to the card. This is causing my credit cards to always report a zero balance. Is this the most effective way to manage my accounts if I'm looking to maximize my overall credit scores?
I did it all the time before coming to this forum 
In my case whenever all my accounts report a zero balance, my scores drop by about 15 points. So you may want to leave a balance of $1 on a single card to report for optimal scores.
@Aarvard wrote:
@Anonymous wrote:I always pay my credit card balance in full the day the charge posts to the card. This is causing my credit cards to always report a zero balance. Is this the most effective way to manage my accounts if I'm looking to maximize my overall credit scores?
I did it all the time before coming to this forum
In my case whenever all my accounts report a zero balance, my scores drop by about 15 points. So you may want to leave to a balance of $1 on a single card to report for optimal scores.
+1 I usually have a small amount report each month but this month had zero balance and my scores dropped around 15 points.
If all my cards report zero, I lose about 10-15 points. If I let between 1-3% report that gives me the best consistent score.
Current Score: TU: 674 | EQ: 722 | EX: 717 | Last Inq. 2/16/15...Locked Up in The Garden