Hi Claire,
There's a few things you can do to change the appearance of your images in Quark. Like InDesign, you need to tell it to display images in full resolution. InDesign overall works much more easily at this than Quark, but it's not hard either.
First, check your preferences in Quark. Under "Display", change the setting for "Color TIFFs" to 32-bit and "Gray TIFFs" to 256 levels. That alone will drastically improve the display of TIFFs.
Beyond that, to get a true high res display in Quark, Ctrl+click (or right click with a multi button mouse) on any image you want to see a high resolution display of. From the contextual menu that pops up, choose Preview Resolution > Full Resolution. Start the Help function in Quark, put in "full resolution" and then choose the heading "Setting Preferences for Full Resolution Preview". Everything you need to know about how and when Quark displays full resolution previews is in there.
Note that Quark stores the previews it builds in the "Preview Cache" folder within the Quark application folder. You'll want to clean this out every so often to keep from filling up your hard drive with what are essentially scratch files.