I'd define a "walk-around lens" as one that has a pretty wide range of focal lengths that cover the middle range slightly wide to normal to moderately telephoto, to cover as many situations as possible in a single lens, and is reasonably compact and unobtrusive. It's essentially to replace your 18-55mm kit lens.
It's arguable that the lens on your list that best meets those goals when used on your camera is the Canon EF-S 15-85mm IS USM UD. It's a little wider than anything else at 15mm, yet still includes nice rach to 85mm. It uses an f3.5-5.6 variably aperture to keep it reasonably compact and be able to offer such a wide range of focal lengths. It's an EF-S lens for crop cameras such as your 450D, Canon mid-grade build with USM and IS. Excellent image quality. Currently is selling for $660 at B&H Photo in NY.
As you know, there are plenty of alternatives...
- A "faster" lens with f2.8 aperture that's not variable... such as Canon 17-55mm, which also EF-S, also has USM, IS and top image quality... Notice the narrower range of focal lengths, it's not as wide (2mm makes a big difference at the wide end, and 15mm is quite a bit extra at the telephoto end). It's also considerably more expensive... currently $1000 at B&H.
- A third party lens such as the Sigma or Tamron mentioned, might be less expensive for similar quality. Some are fast (large aperture), but see the same, narrower focal length range to have fixed aperture and/or f2.8. Non-USM (HSM in Sigma) lenses will be slower focusing, might be less accurate, too. Many have some form of Image Stabilization, too (though you may or may not really need it very much on this range of focal lengths... they call it different things: OS, VC, VR... but it does essentially the same thing as Canon's IS).
- A less wide but longer telephoto lens... such as Canon EF-S 18-135 IS. Often sold in kit, too, it's an upgrade from the really basic 18-55 IS. Less wide, variable f3.5-5.6 keep it reasonable size and weight... but it lacks USM. Pretty good image quality and fairly affordable.... now selling for about $350 (cheaper when bought in kit with the camera, though that's water under the bridge in this case). If your 18-55 is wide enough, this lens might be wide enough for you, too. But if you often find yourself stepping back or wishing for wider with your 18-55, then you might want to consider a wider option.
A two lens kit, instead of trying to do it all with one, opens up other opportunities such as:
- Canon 24-70/2.8L (way over your budget) or 24-105/4L IS (stretching your budget). L-series build quality and very good image quality. Both are larger and heavier, but especially the 24-70.... It's nicknamed "the brick" for a reason!
- Canon 28-135 IS... has been sold a lot as kit lens and so is widely availble lightly used, even practically unused, for very reasonable price.... I see them all the time on my local Craigslist for $250 and less, sometimes as low as $200. That's a real bargain for a mid-grade Canon lens with USM and IS. It's even an EF lens. It currently lists for about $450 new at B&H. It is an f3.5-5.6 variable aperture lens. It's also an EF lens, so usable on both crop sensor and FF cameras.
- Third party also offer 28-75/2.8 and 24-70/2.8 options, somewhat more attractively priced. Autofocus may not be USM (or Sigma HSM), though. Watch for unusually large filter sizes, too, if you plan to use filters such as circular polarizers.
With one of these latter lenses, that aren't very wide on a crop camera such as 450D, for landscape and architecture, you may want to add a wider lens such as Canon 10-22, Tokina 12-24, Sigma 10-20 or Tamron 10-24. That's an additional cost, of course, so if going this route you'll probably need to buy a less expensive mid-range zoom to keep within your budget.
One of the less fast aperture lenses (f3.5-5.6 or f4, for example) should be fine for daytime shooting... but might be a bit challenging to use indoors or in low light. Lenses with IS (or OS or VC or VR in the third party) can help hold the shot steady at lower shutter speeds, but don't help stop subject movement. You particularly might want a good flash with one of these lenses. Or if you do a lot of portraits you might want a faster prime lens such as 28/1.8 or 30/1.4, 50/1.8 or 50/1.4.
So, really, there are a lot of ways to put together a kit...
Personally I use a Tokina 12-24/4, Canon 24-70/2.8L and 28-135 IS, and have avalable faster 20mm, 28mm, 50mm and 85mm prime lenses, among others. I also have several flashes. I use both crop sensor and frame cameras, so I try to get lenses that work on both (only the Tokina 12-24 is technically a "crop only" lens, tho it actually works at least as wide as 18-19mm on full frame).
Right now in my backpack for "walk-around" with 5D Mark II (FF) with Canon 20/2.8, 24-70/2.8, 135/2, 300/4 IS & a 1.4X teleconverter. If I were walking around with one of my 7D's instead (same crop as 450D), I'd change lenses to Toki 12-24, either the 24-70 or the 28-135... Then maybe some other lenses, depending upon what I was shooting. The 28-135 often gives enough reach and is smaller, lighter than the 24-70, and is fine for daylight shooting. I use the 24-70 more when I'm also taking my 70-200/2.8 IS, such as shooting sports, and/or if shooting in lower light situations or wanting larger aperture for candid portraits. If I think I'll be indoors or shooting early or late, or wanting heavily blurred backgrounds such as for candid portraits, I'll add a faster prime lens or two.
Someone mentioned macro.... Though I don't see that as part of the original question. Many zoom lenses say "macro" on them, but really aren't. At best they might be able to do one fifth, one fourth, maybe one third life size....which is close-up but not really macro. However, it's easy enough to add a macro extension tube to get practically any lens to focus closer.
You have a reasonably good budget to work with, though one of the more "premium/fast" lenses might bust it pretty quickly. If you aren't planning future purchases, you might want to choose a less pricey lens and put some of that budget to an additional wider zoom, a fast prime, a flash, macro extension tubes... or several of these items. If this is just the first of several lens upgrades you'll be doing over time, adding to your kit in the future, but more slowly, you might be happy with one of the more premium/fast lenses now.