while this is the first I have heard of the video issue; the lens chromatic issues are all lenses with all digital cameras - when fully open (above I pointed out that you don't really ever use those wide open settings unless you have to) and, in fact, you get different color issues going all the way stopped down so in general with any lens you want to use F 8 to F 11 - it's what the lens was designed for
USE a LIGHT (movie light or add on flash for pictures)
to answer your other questions:
New or used - at this point you will rarely find much difference in new or used; you might get a little break on new at ebay but not much; used you would need a significant difference and most sellers are trying to recoup all te money they spent. If you could find one at $750 (body) or $850 (with a kit lens, more for better lenses) it would be worth it, but think: WHY are they selling it? What sort of guarantee fo you have? What kind of support fo you have?
Is that worth it to you?
starting lenses - Tamron 18 - 270 f 3.5 - 6.3 well reviewed is under 600 with rebate until Oct 19 2011 (Abe's of Maine for 544.95 http://www.abesofmaine.com/item.do?item=TM18270AFC-PZD&id=TM18270AFC-PZD&l=FROOGLE
used you can find it in the 500's -- this should be your all purpose video lens; you might consider (for budget reasons) the 50mm F 1.8 canon around 100 (much lighter and far less expensive than the f 1.4)l; for wide angle the tokina 12 - 24 (F 4.0) or the sigma 10 - 20 ( F 4 to 5.6) are good choices and generally under $500 (don't forget to budget lights and tripod, possibly a camera bag but those are so cheap used, garage sales, often free with purchase of camera
advice on great video capturing = this is 90% technique so practice, practice, practice. Practice following moving objects; practice predicting which way they will move, what that does to focus. Go to high school athletic activities and practice following the action football / soccer / baseball; basketball / tennis / badminton (indoors and smaller distances), swimming / diving (up and down AND sideways); practice following cars in traffic (you on a sidewalk); bicycles, pedestrians at a corner (or if in Portland OR, anywhere on any street downtown, pedestrians ignore corners there); follow river traffic (much slower) or airplanes taking off (much faster); -- do all of this but practice, practice, practice so when the moment comes you get it right. Movement is what kills you in video
you will probably want image stabilization off (most image stabilization systems want to counter any camera movement and when filming moving objects
you will want a video / movie light; trust me on this you can never have too much light
you will want a decent tripod with a head that rotates easily in one direction at a time as well as two directions (sideways AND up and down) to follow action -- and you might want some sort of harness / stabilization system for walking
and read all the magazines you can on video photography (popular photography, outdoor photography, etc) and see websites on it like http://blog.planet5d.com/
which our canonrumors guy was recently interviewed on