You are looking at two different things... An ultra wide angle zooms and a standard zoom.
I'd suggest you consider them separately first... then how they will work together in your kit.
I'm not all that familiar with the standard zooms you are considering... so am not going to try to recommend any of those. If you got a 17-something or 18-something zoom for this purpose, you can complement it with an ultra wide that picks up where the standard zoom leaves off, or have some overlap. Some folks like overlap for convenience, it might mean a little fewer lens changes in the field. On the other hand, it's always nice to maximize your range with whatever lenses you choose, so that you cover as much total range as possible. Gaps between lenses may or may not be imporant. As a rule, they are more bothersome at the wide end (for example between a 10-22 and 28-75 lens), where even a change of two or three mm can be pretty dramatic. With telephotos, a bit of a gap isn't all that big a deal (such as between a 17-55 and 70-200). But If you go with a 24-whatever or 28-whatever as your "standard zoom", you have other choices if you're concerned about the gap.
First, there are now two Sigma 10-20... The cheaper is the one that's been available for some years, has a variable aperature and when I tested one a few years ago, frankly I wasn't all that impressed. It was decent build and IQ, but I felt it was a little soft in certain respects and tended to get halo flares around bright lights too easily. It also is one of the slowest lenses in the category, with f4.5-5.6 vraiable aperture. The new Siggy 10-20 is a fixed aperture f3.5 lens and is considerably more expensive. I haven't used the new lens, so can't really comment, but have seen some really nice images taken with it.
Canon 10-22 has overall excellent IQ and is the best of the bunch handling flare, which can often be a concern when working with an ultra wide angle lens. Frankly this lens is pretty amazing in this respect. It's also about the most expensive choice by a significant margin and it appears the OP is trying to stay within a fairly tight budget.
The lens I use is Tokina 12-24/4. It's quite good, too, though a little less capable controlling flare than the Canon 10-22. I like the 12-24 better than the Tokina 11-16/2.8 because it's a better range of focal lengths and I have little need for f2.8 on an UWA lens (and suspect this is actually true of most folks). And it doesn't hurt that the 12-24 is about $100 cheaper than the 11-16/2.8 (and about $300 cheaper than the Canon 10-22).
Another possibility is the Tamron 10-24. I haven't used it so can't really comment about it.
Pricewise, cheapest are the Siggy 10-20/4.5-5.6 and Tammy 10-24. Toki 12-24 is a wee bit more. The Toki 11-16 and Siggy 10-20/3.5 are a bit pricier. And the Canon 10-22 is the most expensive in this category.
I haven't included even wider lenses such as Siggy 8-16 or more expensive full frame capable Siggy 12-24 here.
Really they are all pretty well built. AF performance won't be all that different, either. I worried about the lack of USM with the Tokina I bought, but it turned out to be a non-issue on an UWA. They don't have to move their focusing elements much to achieve focus, so it's near instantaneous even without USM (or Sigma's HSM). Focus accuracy also isn't critical with an ultra wide, either.... you usually have so much depth of field that any slight error is completely hidden.