Nice. What lenses you going to attach to it?
With these sensors they need to have really high end glass or the upgrade probably won't give the upgrade in IQ you would expect. Saying that the 24-105mm really impressed me to start with better than the 17-55mm F2.8 and has a lot more range, then bought the 24-70mm F2.8 better IQ but its much heavier and less range, use this for all commercial work tho and the 24-105mm as a walk around. Thats a good place to start, 17-40mm is a bit of a dog on FF would skip that and buy the 16-25mm F4 or the 16-35mm F2.8 if you need the extra stop but the F4 performs a little better, any of the 70-200mm will perform well, the 70-300mm F4-5.6 is a lovely lens on FF nice range too, 100mm F2.8 L Macro is a blinder on FF can be used as a portrait lens, macro and medium tele for sports really agile lens. Whats nice is that with the ISo range of the 5DMKIII you can get away with using F4 lenses like we used to use F2.8s just put the ISO up one stop, advantage more DOF disadvantage little more noise and the F2.8 is more versatile but heavier and more expensive.
The F4 trinity is a good place to start. 24-105mm, 16-35mm, 70-200mm. Or if you have enough funds the 2.8 trinity 24-70mm, 16-35mm, 70-200mm.
TBH I like the 70-300mm the IQ is amazing. Saves buying a teleconverter and you can use it native at 300mm at 5.6 without the AF slowing down, I would skip the 100-400mm unless you need the range as a new one will be coming out soon hopefully.
Also couple of other things about FF generally, the FF sensor is nearly twice the size so is much more sensitive to vibration, the mirror is also twice the size and mirror slap is something much more present, so just watch the shutter speed or you might get more blurry images than you would usually, IS helps but worth watching, focal length rule of minimum shutter speed should keep everything in check so 200mm shoot no slow than 1/200s. In terms of depth of field, F4 on FF is equivalent to F2.8 on crop so shooting F2.8 lenses and below can be a challenge to start with, F2.8 might not seem that fast but depending on your focal distance you might only get 1" of depth of field, nailing focus is harder but the AF of the 5DMKIII really helps. With its many modes I like using the zone AF there are 3 different zones so which ever feels good. You will find that 3200ISO is about equivalent to 800ISO on crop so 6400ISO is really useable which is useful!
The AF is complex and this guide which Canon doesn't provide with the camera is really helpful and a good read. Goes through all the modes and when to use them.
http://cpn.canon-europe.com/files/education/technical/eos_1d_x_explained/AF_guide_EOS-1DX_eng.pdf
Its a beast of a camera! Enjoy
