Lot's of good info here already...
If using an AF camera, most of the time you need to get a circular polarizer. Has nothing to do with digital or film, mostly with auto focus, but some metering systems also require a C-Pol.
But, using a linear wouldn't actually "break" anything. It would just cause auto focus accuracy problems (with Phase-detect AF systems, which is what pretty much all DSLRs and film SLRs use), and might also cause exposure errors in some cases.
That's sort of a shame. Linear polarizers are not just typically cheaper, they also often work better than circular.... A linear filter of equal quality can give smoother transitions and can be dialed in for a little stronger effects when wanted.
If using Live View with Contrast-detect AF (which is slower) in many of our Canon cameras, you probably could use Linear polarizer. Certainly might be possible if using manual focus lenses, too. I haven't tried it with my Canon cameras, so can't be sure whether it would mess with their metering or not.
Nearly all polarizers of either type have about the same reduction of light coming through them. Most have filter factors of 2.3 to 2.8, which is up to about 1.3 stops of light lost at their strongest setting.
There are a number of good brands and places to buy them...
I like and mostly use B+W Kaesemann C-Pol. They are very good quality, multi-coated, and have a nice, smooth transition (about as good as it can be with circular).
B+W Pro MRC are also quite good, a little cheaper than Kaesemann.
Hoya Pro 1 with HMC or SHMC (multicoatings) are excellent, too.
Heliopan SH-PMC are also top quality, more expensive than most though.
Singh-Ray is another top brand.
Marumi is a newer brand I haven't tried, but have heard a lot of good things about.
There are others, I'm sure.... Just be sure to look for multi-coating... and use your lens hoods for best results, even though it's a little inconvenient when adjusting a polarizing filter.
There are also a lot of good sources... B&H and Adorama both give discounts, I believe, if you buy multiple filters at the same time. There is also a popular online seller who offers most of the top brands at good prices, but I'm forgetting the name and URL. Amazon might find you some good deals (such as Beach Camera), but may be overpriced themselves.
I believe both your lenses use 77mm filter, so you only need to get one to share between them. And, I'm pretty sure you won't need a more expensive, special "slim" filter for your 10-22 if you get B+W (which are pretty slim even in their standard mount). If you do choose to go to a "slim" in another brand, watch out that some of them don't have front threads, so you can't even cap them when not in use.
Experiment with the C-Pol when you get it. Don't just get it out for sunny day shots... making blue skies deeper and white clouds pop. It's also excellent on overcast days, to help saturate foliage and other reflective surface. Of course, shooting buildings, you'll probably be dealing with window reflections some of the time, too... Might sometimes be useful inside if the view through the window is important.
I just realized this is a really old (2009) thread that's been restarted. Oh well.