I wouldn't get any of them. Not if you're looking to upgrade. If you have to have one of these I'd go with the 28-135. It is a decent lens. It has IS. While it isn't a particularly bright lens it is certainly the brightest of the options provided. So you get your low light that way.
An alternative would be something like the 18-55 IS (It is much better than the 18-55 and has IS.) coupled with the 55-200 IS. 17-85 IS would also work.
Exactly...after your "eye opening" experience with the "L" glass of your father's assortment it seems you want to do more...but with less.
Keep in mind that with the XTI's crop sensor, whatever focal lengths you choose will be "magnified" by a factor of 1.6 as an example a 10-22 would have an effective focal length of 16-35
It may be very difficult to cover the focal lengths you are looking for AND maintain "bright" (large aperature) coverage with one or two lenses and stay within the budget you have in mind.
I use two lenses:
As mentioned the 24-70 is heavy but it does not bother me and it is my daily driver...bright/tack sharp/very high image quality
The 70-200 covers MY needs for "reaching out" and is a definate "winner" in the cost/benefit game. I don't need IS or 2.8 in this focal length and have quality glass at a VERY affordable price
I somehow sense that if you also were able to cover the 24-200 focal lengths with quality glass using one or two lenses, that your needs would be satisfied.
I suspect however that with your backpacking, one of the two lenses I use would not be practical due to size/weight and cost.
So as others have mentioned you should probably consider:
17-55 F2.8 IS (bright wide aperature with IS )
24-105* (you would get more focal reach but settle for indoor flash)
70-200 F4.0L*(non IS version = excellant glass at a bargain price and very easy to carry)
70-300 f4 IS
* represents what I would ultimately choose for you based soley on the criteria you laid out in your post
Best wishes in your search...I would be curious to now what you ultimately decide on...and why