The majority of the work we do at my business is helping small business like yours with their technology needs, and we have migrated many over to their first server environment. It does take some work, depending upon what all they intend to use their server for, but to be honest the most difficult part of the change over is not the actual setup and installation of hardware or software, it is getting all your staff to utilize the server properly and change their file access habits perhaps to saving data on your new server instead of their own computer.
It doesn't sound like you would need a massive server to begin with by any means. I really like the HP ML110 G7 server as it can be very easy for a first server to configure, and very cost effective as well. So for this I will base my example on this server.
First off, you would not have to go with a full-fledged Windows Server operating system to do what you are wanting to do initially it sounds. Installing Windows 7 Professional or Windows 8 Pro on the system would allow you still set up individual user accounts, create shared folders, assign individual share permissions to those shared folders, and also share out direct-attached printers. If your laser jet printers are network-capable (have a 10/100 LAN port) then you can just install them directly on each end user workstation instead of running it through a single server connection, but if not then plug them in to the server and share them out from there.
Quickbooks should have a way of installing onto your server and the software will act just as a server to be shared out to multiple users. This way, your company file stays on your server where it is protected, backed up, and centrally managed. Your end user workstations will work just as they do now for Quickbooks, where it will point to the server for the actual company files.
Your contacts list is also something you might be able to move to the server to make it easier for everyone to access all the same contact information. Is there a certain program you use to keep track of all the contacts?
Now, while you can get away with using just a Windows 7/8 Pro installation on your server to do all these things (and it will save you money), you may also consider going to a full Windows Server 2008/2012 solution. Windows Server 2008 R2 Standard or Server 2012 Standard will allow you to run all of your tasks plus room to grow if you need to add new functionality. In other words, if you wish to set up a domain network, where all user accounts are controlled by the server, or set up additional backup features, website access, or remote access, then you should look more into Windows Server OS. The other benefit is being able to leverage virtualization to help improve your flexibility. With virtualization, you can have little installed on the physical machine, but run a virtual server within it that does everything within your network. Backing up this virtual server is much easier because everything for the entire server is saved in a single virtual hard disk (VHD) file. In the event that your physical server were to go down, you can help eliminate downtime by simply loading up that VHD file onto any other Windows 8 Pro computer in your office running Hyper-V (can be installed on the Pro version at no cost), and starting up the virtual machine again. Instead of possibly being without your server for two weeks waiting for replacement hardware or fixes, you are now up and running again within an hour.