What would you look into for the local window companies? Any reason I should or should not go with a "no name" versus a national brand?
Seems like the approach would be the same as for pretty much any other durable good: verify the reputation of the company, weight that according to how long the company's been in business, and then keep that in mind as you evaluate the warranty that they offer. The evaluation of the company's reputation will include information about how responsively that company honors its warranties.
For reputation, you can look at resources like the Better Business Bureau, Yelp, Angie's List, etc., and that's useful. But even better would be to ask around. Talk to building contractors to see if they have experience with the companies in question, and even window installation contractors (who may have their own agenda, but will at least have more direct experience with the products in question).
You should also ask for references, but take any of that with a grain of salt. Any company or contractor will do their best to make sure the only customers they let you talk to are ones that they are sure will give them a good review. But you can at least get an idea of how good the windows could be, and what kind of customer service the company could provide.
People often say to get three references, but my experience has been that three is often too few. You are more likely to get at least one really honest, critical evaluation (as in "I know you liked this company, but if you had to say anything about what they need to improve on, what would it be?") if you get five or more references. It's more work, but it's probably worth it for something as expensive and critical to the health of a building as windows.
(Full disclosure: I have plenty of times, even after getting several references and following up on them, been disappointed with the level of quality of service I've gotten from a contractor. I chalk this up to the fact that a large proportion of customers can't tell the difference between a good job and a crap job, which makes it impossible for them to give realistic feedback about the quality of a contractor. In any case, references are probably the least-informative type of research a consumer can do.)
You may also be able to parlay the references into additional contacts, i.e. the company that installed the windows, if not the manufacturer, as well as possibly getting site visits to see the installed product. Installers may work with a variety of brands, and can offer you better and less-biased advice about the different manufacturers, including the relative number of warranty claims between companies. Again, more references means higher likelihood of a wider variety of installers to talk to.