Advantages of country TLD vs. .com

I don't think the TLD has a direct impact on SEO, as long as you use good page titles and a readable URL structure.

It's long been a convention to use .com addresses for business websites, as well as near any other site, simply because of the prevalence of .com addresses. But it's now much harder to get meaningful domain names on .com because of how widely used the TLD is used.

A country-specific TLD is quite appropriate in the case that the site is based in that country or is about that country, or the owner or operator is in the country.

All of that to say, if you can get your desired .at domain name, then get it and get to work!

Google, and probably other search engines too, uses ccTLDs as a "strong signal" that a site is intended for a specific country. Using .at, therefore, wouldn't be ideal for what you describe.

So if your target is global avoid .at, but you needn't use .com - any gTLD should do the trick, and probably be cheaper.

Sources:

http://support.google.com/webmasters/bin/answer.py?hl=en&answer=182192, especially:

ccTLDs […] are tied to a specific country (for example .de for Germany, .cn for China), and therefore are a strong signal to both users and search engines that your site is explicitly intended for a certain country. […] We also treat some vanity ccTLDs (such as .tv, .me, etc.) as gTLDs, as we've found that users and webmasters frequently see these as being more generic than country-targeted"

Edited for relevance, bold emphasis mine.

I'd say get both, if you can! And use 301 redirection for the secondary(s).

I am bemused at the number of times I've given .uk URLs and email addresses to people, who've immediately read it back as .com. A good job, I usually hold the .com domain too.

.com is so ingrained in people's brains. Pretty much any other TLD (or ccTLD) has potential for confusion!