The price you use for what specifically?
The price to use for determining what coin to switch to.
The value of coins on hand when reporting miner proceeds? The value of new coins as they are mined before maturity? The value to compare against other currencies for mining profitability calculations? Please clarify.
The value of new coins before maturity, plus mature coins that haven't sold yet.
I'm guessing, bit it sounds like you are saying that while mining coin A, you decide to keep mining coin A by comparing (every minute?) the price of the buy order for A that is X coins from the top of the buy order list (where X = on hand plus estimated proceeds from several minutes of mining), combined with coin difficulty, to determine if the current coin is better to continue to mine than other coins at their respective price/difficulty, using the same price methodology for the other coins? Is this correct?
Yes, that's right.
Also, what price do you use when reporting the freshly mined coin value to miners?
You mean, on the webpage stats, for the BTC estimates? I use the last sell price.