Before we look at the bodies, let's talk about lenses. In my opinion the lens is about 2/3 of the hardware equation and the camera body and all other accessories are the other 1/3. None of the lenses you mention are stellar performers, but the EF 75-300mm f/4-5.6 III has the worst reputation of any Canon lens currently in production. I would forget about it in any kit you plan on buying, even if it only adds a few dollars to the price. It's just not a very good lens. On a crop body sensor the EF-S 55-250mm f/4-5.6 performs much better and is not that much more expensive when bought in a kit than the larger, heavier 75-300. For a more in depth explanation of the differences, see Canon 75-300mm f4-5.6 USM or 55-250mm f4-5.6 IS lens?
The current EF-S 18-55mm f/3.5-5.6 IS II and EF-S 18-55mm f/3.5-5.6 IS STM lenses are much better than some of their predecessors, but they are still on the lower end compared to many other lenses available. The best value in this lens category is the Tamron 17-50mm f/2.8 Di II. It has comparable optical quality to the Canon EF-S 17-55mm f/2.8 IS. The Tamron runs around $500, the Canon is about $1,100. For that extra $600 you get IS and better feeling build quality. I've owned the Tamron for over 4 years and used it heavily for the first 2-3 years I owned it before going full frame with my wide angle body. It is still just as good as the day it was new and, unlike any Canon lens over one year old, is still under warranty until early next year. There is also a Tamron 17-50mm f/2.8 Di II VC (Vibration Control, Tamron's equivalent to IS) for about $650. Some reviewers have placed the image quality about equal to the non-VC version while others, most notably The-Digital-Picture (who never completed the partial revue posted on the website), say it is much softer. My guess is that he got a bad copy of that lens and never followed up with a replacement, something he has done several times when receiving a Canon lens that performed below expectations. I have no personal experience with that lens.
The EF-S 18-135mm f/3.5-5.6 IS (either the original version or the new STM version) are a little better optically than the 18-55mm kit lenses and is worth the difference if bought as a kit. But since your emphasis seems to be on portrait work, using a lens with such a narrow aperture has its drawbacks.
For the portrait work you do, a prime lens such as the EF 50mm f/1.4 would serve you much better by allowing you better image quality and a wider aperture that would give much shallower depth of field. The EF 50mm f/1.8 is much cheaper, but the build quality is also much lower (I know several friends who have broken the plastic mount), the bokeh (background blur) is much harsher at apertures other than f/1.8, and the manual focus is virtually unusable.
Now, on to the two bodies in question: The EOS Rebel T3i and the EOS 60D. The image quality is very close for both of these cameras as they are built around essentially the same sensor. The major difference between the two is in usability and handling speed.
- The 60D has a larger viewfinder that is brighter than the T3i's.
- The 60D will shoot at 5.3fps compared to 3.9 for the T3i.
- When saving images as RAW files, the 60D can take 16 images @ 5.3fps before the buffer is filled, while the T3i slows down after only 6 RAW files @ 3.9fps. With JPEGS the 60D can go 58 frames compared to 34 for the T3i before their respective buffers are full when shooting in burst mode.
- At 59 milliseconds, the shutter lag of the 60D is less than 2/3 of the T3i's 90 milliseconds shutter lag.
- The 60D, like other Canon prosumer and professional bodies, has two control dials that can be used simultaneously to change different settings without taking your eye away from the viewfinder. This is especially valuable when shooting in manual mode as you can control the shutter speed with the main dial just behind the shutter button and the aperture with the quick control dial on the back of the camera. When using Av or Tv mode, the rear dial controls exposure compensation while the front dial controls either aperture or shutter speed. The T3i has only the one main control dial just behind the shutter release button, and thus requires delving into menus to change many settings that may be changed with the push of one button and a twist of a dial on the 60D.
Ultimately you must decide what your budget will allow and work from there. The faster handling of the 60D will come in handy especially when shooting children. If I were making the decision for myself, I would buy the 60D kit you have mentioned and an EF 50mm f/1.4 lens or possibly an EF 85mm f/1.8. That list will run about $1,350. If you find the need for more reach than the 18-135mm lens provides, the EF-S 55-250mm f/4-5.6 IS can be found for well less than $300 with a little web searching. If that exceeds your budget, the T3i is also available as a kit with the EF-S 18-135mm f/3.5-5.6 IS and you can throw in the EF 50mm f/1.8 and come in at around $900.