The reason I said the Canon 24-70 would be large on your 600D is it's size. I have two rebels and it is definitely not balanced very well on those bodies. It is a huge lens and you will be a little lens heavy. I suggested the Tamron without VC because it is crazy sharp. The VC version I have heard is not as sharp and I don't really think you need IS in a lens of that nature. It is light and focuses fast enough to catch my kids in action (5 yrs old). I used it for about 90% of my wedding photos and stuff before about November of 2011 due to focusing issues on my Canon 24-70mm. The Tamron took a trip to the service center right after I got it and was perfect when it came back. I have had horrible luck with Sigma lenses and focus shifting, but other have had good luck. So take your choice.
Yes UWA is ultrawide. I have a friend with the Canon 10-22mm and it is a great lens. I got my Tokina 12-24mm on a deal because I have always wanted to try one and it is a great little lens. Had a constant f/4 so I am happy. So, I am not going after the Canon UWA anymore. It is also about $150 to $200 more. Here are a couple shots with my Tokina recently. I am not a landscape photographer by any means, but it is fun.
As for the Canon 70-200 f4 L, that's what I was talking about. This one
http://www.the-digital-picture.com/R...ns-Review.aspx is about $640. The Tamron
http://www.the-digital-picture.com/R...ns-Review.aspx has a rebate also and is about $414, then you have a Tokina 12-24 at about $525 or the Tokina 11-16 at $659 or the Canon 10-22 at $756. All prices can either be found on B&H or Adorama.
If you were to get the Canon 10-22 at $756 and Canon 24-70 at $1269. If it were me and I was just starting out, I would get something in the paragraph above and then if I decided later on, upgrading is always an option. I would have been very happy with the first kit when I first started out and would probably still be using most of them. I only have the Canon 24-70 from a gift over the holidays of last year otherwise I would still be using my Tamron all the time. The 24-70 sometimes just is not wide enough to shoot stuff indoors in tight quarters because with the 1.6x crop factor is it a field of view from a 35mm area. I mainly use it outside. Hope that helps.
Here are a couple examples of why I say it would be large on you 600D. Both are on an XTi or 400D I think it was. Canon on left, Tamron on right. Photo taken with the other lens. Canon is also much heavier.