Suitable database software for small business
For something simple like what you have, I would highly recommend Google Docs or one of variants. It's basically a spreadsheet where everyone that you give permissions to can edit at the same time. Everyone can see what everyone else is doing, so there aren't many conflicts.

A SQL database would certainly support simultaneous accesses, but I think it's overkill for what you're looking for. You would need to build an application on top of the database just to use it. If none of you are willing to spend the time to write and maintain this application, I would not do it.