Opinions will certainly vary on this question. It surely does depend on what you want to accomplish with the lenses, also.
First off, I'd forget the 10-22, and question the 17-55.
The 10-18 is optically superior, has STM focusing for video, includes IS (image stabilization), and is 1/2 the price of the 10-22. Its limitation is slightly slower aperture at all focal lengths.
The 17-55 has always suffered from Residual Spherical Abberations, which simply stated means it will miss focus, at close distances, when stopped down. To be fair, you have to really stop down AND be really close for it to be an issue. Using f/4 at 5' is not going to be a problem. Using f/11 at minimum focus distance will be a big problem. Better glass is available, if you are willing to pay for it.
The 18-55 STM is a very good lens, optically. It is a tad slow to focus, and slow of aperture. It is also capable of 1:1 macro with an extension tube, which is 1/4 the price of a dedicated macro lens.
Full disclosure, I own the 10-18 and 18-55 STM lenses. I intend to keep both of them.
If you are willing to spend a bit more money, pass on the 18-55 STM and get the 18-135 STM. I got the 18-55 STM for 2 reasons: it is cheap, and I already have the 24-105 STM for use on my 6D. The 24-105 STM is also an option for you, but it doesn't have the focal-length range of the 18-135 STM.
The 15-85 covers a nice useful range, and you may be able to pass on the 10-18/10-22, if 15mm is wide enough for you. Honestly, 10mm on crop isn't wide enough, frequently. That is me, though.
Back to the 17-55. It really is your only choice if you want an almost-wide enough, almost fast enough zoom. I don't think f/2.8 is fast enough to justify the expense of this lens. But there are few choices for wide, fast glass for apsc cameras. The Sigma 18-35 f/1.8 is huge, heavy, and expensive. I think the only other options are even more expensive: 20 f/1.4A, 24A, 24L II, 35 IS (or 35L or 35A). At this point it is cheaper to buy a 5Dc and 28 1.8 if you want wide and fast.
At this point, I recommend the 10-18 and 18-55 STM efs lenses. They are extremely good bargains for the IQ and features you get. After that, choose the appropriate EF lens for whatever application you have in mind.