Extremes are generally where cameras differ- and the more extreme, the more that they cost.
For your budget - it does sound like a Rebel- entry level. Generally speaking, you really want to get as new of a body as you can- so that you can leverage as much tech as you can. Straight out of the camera, a t4i should fare a little better than a t3i, but it's a small amount better- especially if you are depending upon Straight Out Of Camera jpegs. One should typically buy the newest body that they can afford- to get as much out of the camera- because you may buy lenses as needed- but most people upgrade bodies less frequently. For max low-light capabilities- you are looking at full frame- and a lot more money.. T3i or T4i should be similar- but like I said- slight edge to the t4i.. Some will say that you can make up for an older body by going with faster glass- but faster glass generally costs more - and then only that piece is able to do more- whereas if you get a body that can do 6400 as well as an older body that can do 3200 as well- well- that 6400 iso- you can use it with each piece of glass you own.
With either body- if you are dealing with the extremes of low light- go with a faster prime and you might gather enough light. Combined with even a slightly better body- it might make a difference.. So, if you get like a 50mm f/1.8 and pair it with a camera- you might get low light shots without adding flash. If you are not concerned about using flash- the lens matters a lot less. A t3i should be able to handle about 3200 ISO decently, and a t4i- maybe 6400. If you use flash- you'll be using slower ISO speeds anyways- so, it won't matter.
My suggestion would be to re-evaluate how much you are willing to spend- and budget for the better solution rather than buying less and, well, getting less.. BTW: T2i, T3i, 60D, and 7D all basically have the same sensors with the same ratings.. T4i's sensor is rated slightly higher by Canon in a couple of areas.
Initially, I'd suggest getting the kit lens- and try it out with your camera for a while to know what it is capable of.. Then get the appropriate glass to fill unique needs that the kit lens does not handle well. For a t3i, get the 18-55 IS kit lens.. For a t4i, I highly suggest the 18-135 IS STM lens.
EOS 5D III, EOS 7D,EOS Rebel T4i, Canon 70-200 f/2.8 IS II, Canon 24-105L, Canon 18-135 IS STM, 1.4x TC III, 2.0x TC III, Σ 50mm f/1.4, Σ 17-50 OS, Σ 70-200 OS, Σ 50-500 OS, Σ 1.4x TC, Σ 2.0x TC, 580EXII(3), Canon SX-40, Canon S100
Fond memories: Rebel T1i, Canon 18-55 IS, Canon 55-250 IS, 18-135 IS (Given to a good home)...