Verdana and Arial are extremely safe to use. They should be pre-installed on your computer. But like I mentioned in your other thread, there are many services for web fonts that work cross-browser and are more than safe to use. If you have more specific questions regarding fonts or typefaces, I’d be more than willing to help you (same goes for you @dfogge).
Sometimes where your scripts are placed will cause the page flash. I’ve also encountered older versions of jQuery causing the issue.
When it comes to Google web fonts, I would advise not using their library. Google is in the business of making money and not at all about the quality of their web fonts. At the very least, I would go with Typekit which I’ve mentioned in your other post.