1 x desktop Mac, that can hold all of our images and use as a base computer - I would rather not have to pay for a server if I can help it.
Fortunatley for you, Apple don't currently make servers, so I can't tell you not to be such a
tightwad and go buy a server.
However, although you can indeed buy the "server" software upgrade for OS X via the App Store for not very much, you would be very stupid indeed to run it on a machine with only one internal hardrive. You should be storing your data on a RAID mechanism and then implementing a robust backup routine on top of that. Doesn't matter if OS X itself boots off non-RAID, as you can always re-install that.... its where your data is stored that matters.
3 x Mac Book pro or Air, that can link together to share database contacts, that need to be updated in real time. (A database that holds names, emails and client notes, as well as invoices and inventories).
What's your technical know how ? OS X Server comes with a built-in webserver and MySQL (I think, re:MySQL). A bit of scripting could find you up and running with a shared database.
Otherwise there are probably alternatives to off-the shelf GUIs like Filemaker.
Run the third party software though a Windows Parallel Operating System on a Mac.
Try it on your laptop, most business stuff should work fine in Parallels/ VMware. Since for all intensive purposes the software can't tell the difference as long as you give the virtual machine enough RAM and access to sufficient processing cores.