First, read pgary's site, its awesome. Second, look for the sticky threads in each forum that are relevant to you, e.g., Miles Buzz, American Airlines, and later on, perhaps specific hotel programs or other airline forums. Also keep an eye out for any thread that has the word "consolidated" in the title. Let me say I am also a newbie, but I have spent a good amount of time reading on this site. So let me take a shot at your questions, one by one:

• is there a 'best' FF program / airline?
  NO, there is only a "best" for you. Variables include where you are located, where you like to travel, what aspects of the FF program are most important to you (i.e., is it the mileage build up, or some of the many and varied elite status benefits?), etc. Continental is rated very high by one of the premiere experts in the field, but honestly, all of the major alliances have pretty good programs if you are located in one of their hubs. If you like American,
  (and remember that with American you are actually getting benefits from all of the One World Alliance members) are conveniently near one of their hubs, and already have Platinum status, I would stick with it. I am AA Plat as well, and really really appreciate the benefits I get from that status compared to two years ago when I had no status. Aiming for Executive Plat this year for sure.
  
• is there a 'best' credit card?
  Again, depends on what you will do with it. First decision: miles or cash back. Since you plan to travel, miles seems like the way to go. If you checked every thread asking for the best card from the past year, you will probably note that the Starwood Preferred Guest (SPG) American Express card receives the most recommendations. There is a reason for this: it is really good. Solid initial miles bonus (10K miles, + 15K miles after the first $15K in spend within six months), low annual fee (waived the first year, $45 after that), flexibility in that you can transfer to most mileage programs including AA, and a 25% bonus in miles when you transfer 20K points at one time. (i.e., transfer 20K points to AA and they actually transfer 25K points. Hard to beat that.) Also, they are associated with one of the better hotel loyalty programs around.
  
• can one buy miles through brokers? I've seen online some offers but am not clear whether this is legal or not?
  I know nothing, but sound shady.
  
• what is the average value of a FF mile?
  2 cents per mile. Others will no doubt contradict me, but this seems like the most frequent value applied. Some programs have a slightly different value scale. You will not that this 2 cent value reenforces GK1998's recommendation about US Airways doulbe miles purchase offer. $1400 for 100,000K miles means a 1.4 cent per mile purchase price. Pretty good, if you fly US Air. Now, if you are talking about building up miles and status via flying, such as mileage runs, then the standard "good deal" is about 4 cents per mile, all in. In other words, a good mileage run only costs you 4 cents per credited mile, once all costs are taken into account. (ticket, taxes, fees, etc.)
  
• is there a way to charge mortgage payments to credit cards?
  Depends on your mortgage service. Most don't take CCs. You can look into a service like ChargeSmart, a broker that charges you a fee for helping you pay your normally unchargable bills via credit card. But the fee structure, which is a bit questionable, will usually cost you more than the value of the miles you would earn. I have $630 of recurring bills on my credit cards, just not the mortgage. The key: check ALL of your bills. For me, Geico, Netflix, AT&T, Atlantic Broadband, and David Barton Gym all take a CC without any "convenience" fee added.
  
• I realized only now that I have with AA Platinum Elite status ... never knew. I read the various benefits associated with it - but how do I get them? e.g., preferred check in; upgrades, more miles on certain elite eligible flights ... none of that I ever did get automatically. So do I need to each time wave my Citi/AAdvantage Platinum card and say what I want (presuming I always know what I am eligible for)?
  Minor question here: Having the Citi AA Platinum card does NOT mean you are a AA Platinum member. AA Platinum status is granted entirely separately. You may already know that, forgive me if I am not giving you credit for that knowledge, but the way you transitioned there to the credit card makes me wonder if you got the programs confused. Now, on to the actual question. Make sure you have an online AA miles account. You don't have to have one registered, but it makes keeping up with this so much easier. Whenever you make a reservation, provide your AA number. This will give you benefits immediately, in that certain fees get waived, and your boarding pass will have Priority Access Platinum Member printed on it. Keep your AA Platinum Member card handy with you just in case. When you want to use on of your 500 mile upgrades, call a few days before the flight and ask for it. You will be notified before boarding if you got it. For security point and gate check in, look for the priority access signs. As long as you gave your FF number to an agent at some point, you will get the miles bonus. Check it on your account to make sure, call if you didn't get it. That's it. You get benefits.
  
• any other tips?
  Read Flyer Talk.