The easiest way I’ve found to test multiple versions of IE is TredoSoft’s Multiple IE, it installs whatever versions you’d like to keep active on one PC (or installation of windows in bootcamp or something similar, if you’re testing on a Mac), it’s free and I haven’t run into any specific differences between how a page renders or behaves there and in a ‘conventional’ install, although apparently there are some outlined on their site.
As far as process, I usually design for Firefox just like you do bumpley, mainly because all the great extensions that are out for it make the initial design portion so much easier. (if you don’t have Firebug check it out)
Every couple of hours or so I’ll open what I’m working on up in IE7 to try and snuff out any problems there while they’re fresh, the same with Safari which can have it’s own quirks. I usually wait to tackle IE6 until I’m pretty close to done, partly out of dread and partly just because it’s easier to make the necessary fixes once things have solidified a bit. If there’s a lot of javascript, I’ll check more often since I run into more compatibility problems there and the error messages are notoriously vague.
Before releasing a site I’ll try to check it out in everything I can get my hands on, but always check Firefox 2, an older version of Safari, Chrome now, Opera, and at least one phone. Hopefully by this point it’s fairly painless but even if you’re not offering full support to something it’s good to know what the issues are.
As an aside, I don’t see any way a professional organization could ignore IE6 at this point. We’re not talking about a fringe browser, depending on your audience it still accounts for 20–35% of users. So at a minimum you’re telling 1 in 5 to “gtfo” rather than spending an extra hour or so making your design work in IE6. It doesn’t seem like a good choice for the firm or their clients.
stats for W3Schools which represents people interested in web development so is probably the best you can reasonably hope for
stats for theCounter.com which is probably closer to a non-tech group you would need to look at for any sort of wide spread audience or e-commerce
If you’re interested, Yahoo talks a lot about how they decide what to support and how. Their Graded Browser Support seems to be becoming something of an indicator for how things are “in the wild”...