Jenny,
In addition to what Michael said, you may use Illustrator (or a similar application), and you should consider whether you are having things printed by a printing company (using CMYK) or you are having them printed on office printers (more likely from what I gather).
In the former case, you may consider creating the artwork using CMYK colours for greatest possible colour consistency. In the latter case, you are (probably) better served with RGB colours. In Illustrator this is called Document Color Mode. CMYK colours are inherently duller than RGB colours, so if you have the best/brightest web version as top priority, you should use RGB in any case, knowing that the printed stuff will be a duller representation, unless you have (access to) a special printer that has more colours than CMYK; in this case, RGB is also the obvious choice.
Apart from that, you may consider creating the artwork with points/pixels as the unit, and set it at the largest planned size in pixels. This is especially important for crispness of non photo raster images such as PNG24 (which is better than PNG8 and GIF): when you create the artwork for web and similar, it is important that you fill whole pixels to the highest possible degree.
Illustrator actually has pixels as a unit identical to a point and equalling 1/72 of an inch, which may be a bit confusing until you get used to it.
For actual logo, and other artwork, creation in Illustrator, you may ask in this forum: