Yes, unless you use web publishing. WIth Web publishing, your client machines can use a web browser to access the database. This is an option that takes quite a bit more effort to set up, so don't make that choice without doing some careful research first.
There is a volume licensing option that can save a few dollars when buying multiple copies of FileMaker Pro.
Your user base is right on the tipping point between having to use server or getting by with using FileMaker Pro as the host for your shared database. If you host with FileMaker Pro, you can have up to 9 other users linking to your database at the same time. There are many other reasons for investing in Server so don't take that as a recommendation to not use server. Research the features and costs and then choose what works best for you. We have the same size userbase here and find Server's additional features to be well worth the extra dollars.