Ok let me give you an honest answer since a lot of these answers are done by people owning lot's of the coins, or being involved in the coin, or having benefits you mining or buying a specific coin.
When a coin is most profitable to mine... you are actually too late. When you want to make money with limited hashing power Always mine 0-day coins. How stupid their names are, or how silly/limited their announcement is.
Always look at the launch, it should not be pre-mined too much. A little for giveaways is ok, to attract attention to the coin. When a launch goes bad by DDOS attacks they are probably doing this themselves so they can pre-mine after launch. In my opinion one of the demands of bitcointalk should be that all coin announcement should be pre-announced to give everyone an honest chance. But hey... who am i. If a launch should go bad they should re-launch it another time. But this almost never happens.
Most coin-devs want to mine a lot of coins themselves the first few days, and it's not in their benefit attracting lot's of miners bringing to diff up too soon. What they do is make a fast , small announcement without much graphics or any other fancy stuff. Then after a few days they edit the post and make it more attractive so many miners will mine, pump up the diff. And then the dev (and the first day miners) can dump the coins on the first exchange it hits.
99.9% of all coins are not made for a longer period of a few months. What also happens is that they let the coin die, let all people sell their coins for peanuts and buy all the coins, and then jumpstart the coin again after a few weeks (like a re-launch) and then sell it when it's worth something.
There are very little announcements for coins that are actually going to be worth something in the future. If i would make a guess i would say the Ron Paul Coin (since Ron Paul will run for president if he can, and he has spoken positive about the RPC) and the DGB (digibyteCoin that has a lot's of devs and really tries to make it a coin with Merchants).
Hope this helps.
+1 for a genuinly smart answer. I think it's something you should learn, rather than teach, but props for being someone else who gets it.
I mined KDC, Cash, and NyanCoin early on, and have seen the difficulty rocket. Such faith I have in one of them I'm throwing everything I have or can afford at it. Sometimes you just know. There's certain things to look out for. For me a strong dev team can ride out the pumps and dumps, but at any one time you know you're holding both trash and treasure, and it's your task to know which to sell and which to hold.