I think HTML5 is just fine to use today, for the most part. There are a lot of elements I would ignore, but putting the HTML5 DOCTYPE on valid HTML 4.01 Strict or XHTML 1.0 Strict is a perfectly fine practice. Adding in a sprinkling of the well-supported HTML5 elements is also just fine. (That thread TehYoyo linked to provides a number of points from all sides.)
I would definitely avoid a Flash-based header. Unless you know what you are doing and add accessibility to your Flash-based header (which is rather tricky to get really good, even for seasoned developers), it can be poor in terms of a lot. There isn't much Flash can do (for a header) that you can't do with good ol' HTML and CSS (and MAYBE a splash of JS).
I would take a look at it in IE6 and IE7, just to make sure it is usable. However, making sure it looks exactly the same as it does in the other browsers is a bit silly at this point. Really, your site should be functional all the way back to IE3, but it's a bit silly to go that far back in testing.
Also, I wouldn't rush getting your site online, depending what it is. You can have a bad release. There is no reason to start scoring SEO "brownie points" now, because any major site change completely changes what SEO points you would get. Wait until the site is at a reasonable point of completeness before getting it on line. Throwing up a one page "under construction" site is going to do you more harm than good.