First the camera body.
My recommendation is to go to a store and pick up both cameras.
Understand what your hands are telling you how they feel.
An uncomfortable camera will be one you will leave home.
Also, a camera that is too heavy you will leave home.
If your hands tell you a camera is not right for your, listen to them.
It does not matter how good of a camera it is, or what features it has, if you always leave it home.
You can only take pictures if you have your camera with you.
That said, if the T3i and 60D both feel comfortable, and this is your first DSLR, I would then recommend looking at the less expensive one. You might want to even consider a T2i as you will get the same image quality.
Once you get into photography, you will get a desire for more expensive equipment.
If you buy a camera and turn out to not like photography that much, then any extra money would be a waste.
Either way, saving some money on the camera body would not be a bad thing.
As for lenses, I would recommend getting the 18-55mm IS and the 55-250mm IS combo.
While these are not the best lenses in the world, they seem to give great performance for the price you pay for them. These are for learning more about photography and finding out what you want.
They also both have IS on them. What this will do is allow you to take a longer exposure.
Cameras need to be absolutely still in order to take good photos.
Your hands are generally not stable enough at longer focal distances such as 250mm or 300mm.
The exception to this is if you take a photo that is quick enough, the shaking from your hands does not have time to affect it.
If this is a beginning kit to get into photography, then I recommend keeping it to the basics.
Once you have mastered what you got, then and only then, think about expanding to something else.
Any money you save now will also help you later as no matter what you get now, you will be wanting to replace it later.
Canon 5DIII, Rebel XTi/400D
Canon EF 16-35mm f/2.8L II, 24-105mm f/4L, 50mm f/1.4, 70-300mm f/4-5.6 DO, 85mm f/1.8
Sigma 150mm F2.8 EX Macro
Sigma 10-20mm f/4-5.6 EX, Canon EF-S 18-55mm f/3.5-5.6 II
Canon 430EX II
Opteka 13mm, 21mm, and 31mm extension tubes
Vivitar 50mm f/1.8 for OM System