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I don't want Google to think I'm spamming them with the site under multiple urls.
Should I write a robots.txt to tell spiders (google's in particular) not to spider the site under the old url?
If so, how would that code appear in the robots.txt file?
If not, is there a better way to deal with it?
In your case, if you add a 301 to olddomain, all your brochure visitors to olddomain will get instantly redirected to newdomain, so you won't have to tell them later which domain to go to. Googlebot will also get instantly redirected to newdomain, and they'll stop spidering olddomain.
You should also contact all your inbound links and get them to change to newdomain.