Segoe UI is not for sale, and only available pre-packaged with certain Microsoft products. Therefore, if you don't have it already, buying a copy of Windows 7 would be a legitimate way of obtaining Segoe UI for use on the computer you install it on.
Once you have a legitimate copy of the font in your possession, feel free to use it to create whatever graphics or designs you like, including your logo. (Fonts are licensed like software, so a font license does not specify what you can do with artwork produced using the font, just as Photoshop's license doesn't specify what you can do with artwork produced using Photoshop; as long as you legally are entitled to have the font installed on your computer, you can produce any artwork you like with it).
However, embedding the font (such as by including it on a website with @font-face) would require an additional license because it would involve making and distributing a copy of the font (and providing the font file to other people's computers) which most certainly is restricted and subject to the license of the font. And you won't be able to buy such a license because Segoe UI is not available for this.
Therefore, for online or any other embedded use (such as in a PDF document, when embedding the font), I'm afraid you'll have to look for a substitute font instead.
You could if you wanted to, specify "Segoe UI" as the first choice in your CSS stack, as many people will have the font pre-installed by virtue of it being included in Windows.
For fallback, you could license any font that bears a similarity to Segoe UI (which in turn bears similarity to both Frutiger and Myriad). Or you could go for a free alternative. The font M+ 2p is a free font that's an alternative to Frutiger and/or Segoe (sample here).