you should use a common font, because majority computers wont have the "unique" font downloaded, and your font on your site or wherever you are using it, will come up as an error because the font cannot be found.
In the end it's all up to your judgment, really. Since you don't mind doing either one, no one can really stop you from trying out either. You just have to weigh things carefully.
have someone design your logo first, so you have everything sorted before you actually complete the finish product of the logo. my suggestion is to search for unique fonts and than download them, a good site to use is www.dafont.com which has almost every font suitable to any logo. You can than design your font from the logo and use unique imaging and design
To echo several replies, go with the one that suits your business best. If it's a font that comes with the computer or program, no big deal. Not many are aware their computer comes with more "fancy" fonts than Comic Sans or Papyrus.