This camera will be fine for your needs, but I would beware of buying from this shop. Something that's $150 cheaper than you'd get it on amazon or b&h
is probably a grey import and won't have a US warranty.
And no website, EVER, has all 5* reviews
And it's also registered to an apartment block in Brooklyn. May be genuine, but when an internet retailer doesn't give a geographical contact address, suspicions are raised.
The only real improvement this camera has over the T4i and T3i is better video. There's little difference from the T4i and, really the T4i was only a minor improvement on the T3i (mainly in the video having continuous AF
Interesting that b&h have discontinued the T4i for the T5i but they still sell the T3i.
I should say I have the T3i and am very happy with it. However, what makes the picture is mostly due to the lens not the camera so it's better to have a lower spec body and better lens instead of buying the best body. And lenses are the money pit.
So you could get a genuine t3i and 18-135 which should cover most of your needs. The T3i isn't perfect for video, but if you're not taking video that won't be an issue.
Alternatives include the Nikon D5100 with a 18-55 lens. Nikon don't seem to have an 18-135.
Sony A58, again with the 18-55
Pentax K-50 with 2 lenses
There are various other Nikons, Sonys and Pentaxes.
Really, at this level, all these camera bodies have reasonably similar performance so 95% of the time you won't see any difference. Some are better at video, some have better sensors for low light (typically nikon) but otherwise there's not a whole lot to choose between them. Any differences are in the lenses, and you may have to read some reviews for those.