I have to agree with Ryan about the LCD screen and limitations in LV for the Mark III...
The LCD is HORRIBLE for viewing images, checking focus, etc ,etc,etc,etc...
BUT, once you put the images on your PC and look at them, you will see why it is a 1D 
the files are VERY impressive. AF is very impressive. not as good/customizable as the 7D...but it is a 1D to the core, and the 7D will never be(not bashing the 7D, I have owned two over the years).
The only reason I sold the 1D3 for a 5D2 was for the better IQ, full frame, and better high ISO performance....but I also stopped shooting sports/action so there was no point in keeping the 1D3.
Honestly, its pretty hard to go wrong with any 1D..imho...and also once you get a 1D a gripped xxD or xD body will never feel as comfortable, or give you a big smile every time you snap a shot..lol
the newer the better, also IMHO, but even the classic,II/IIn are still going strong...and I will probably add a Mark IIn to my gear list when I get back into sport/action shooting..(only reason I am going with the Mark IIn over the Mark III is that I dont need LV, or a body 2x the cost of a Mark IIn for the little bit of action I shoot..may even "settle" for a Mark II...) 
Good luck!