Setting up a separate dedicated server could be quite handy for you not only to help clean up your current network configuration but to allow for improved efficiency and room for future growth. As stated above, I'd suggest looking at Dell or HP for pre-built business class servers.
There's a few things here I wanted to ask before further suggestions:
1) Domain or workgroup? It sounds like the way your network currently is setup is workgroup. This means there is no central computer that is managing all the user accounts, passwords, logins, etc. User accounts are created on the individual computers only. This is most common for small home and business networks with up to ten computers. Once you get beyond that, workgroups get very complex and may even stop working properly. I'd highly recommend at this point planning to implement a domain controller as part of your new server. Set up a virtual machine on the new hardware running Server 2012 R2 and set up the Domain Services roles for creating your user accounts, managing permissions, etc. However, this will also require that the computers in your network are running the Professional version of Windows to join to the domain, so there may be some added cost and complexity there if you need to upgrade licenses or computers.
2) Quickbooks through VPN? I'm a little confused with how you described needing to set up your quickbooks. Do you have two computers locally within your office that need to access Quickbooks? VPN is a remote access technology for people to connect to data or network resources within your office while they are outside the network such as at home or in another town. If you have two employees that will be local in the office needing to access QuickBooks on two computers, then the simple solution is just setting up QuickBooks with Multi-user mode. This allows multiple people to open and work with Quickbooks simultaneously. You can put the main part of Quckbooks and the server database application on your new server, and install the Quickbooks software on each of the other desktops still, connecting back to your server.
3) Proper spacing and resource management? Setting up a simple office server can actually be pretty cost efficient especially if you are doing lightweight work. For example, if you have less than 2 TB of storage space and only need to run a domain controller and file storage, then there is really limited resources or storage capacity needed. However, it sounds like you have more than that which will need to be running on your server. Domain controller, file server, QuickBooks and other application server, plus a database for your workstations. I'd recommend looking into Server 2012 R2 Standard at least, with two virtual machines. One VM would be your domain/DNS/file server, another would be your application server (Quickbooks and database). You can split these out even more for better resource management but that will be more expensive as it requires additional Server 2012 R2 license and hardware resources. But my biggest suggestion is don't try to skimp by! I've seen many places that have ended up trying to save a few hundred dollars and got "just enough" for what they need. Less than a year later they are frustrated because their brand new server isn't powerful enough to handle some new things they want to do, and they have to buy another.