Which facet of this do you need help with? What you describe is a very broad scenario, and one with many options.
You say you have no experience in network design and administration. Does this mean that you will be responsible for hiring an outside company to do the installation and configuration, or are you expected to attempt this yourself? If the later, I'd highly suggest you reconsider. No offence meant, but designing and implementing a 60-node network isn't something that you just read up on and then go out and do.
Some (totally random) thoughts:
- Will wireless be involved?
- Are you going to have a company Email server on the network? If so, and assuming you'll be using Microsoft products, you'll need someone who know how to build and maintain Exchange servers.
- What other data needs to be centrally served? Do you want to use server versions of your actual applications, or will you install stand-alone versions of your applications on each workstation and just serve the data?
- Do you have people who know how to configure and administer Active Directory? With 60 or so seats, this obviously won't be a workgroup.
- Will you want or need users to have remote access to the network? VPN and the like would come into play at that point.
- Do you plan on running a Web server which needs to be accessible to the "outside world"?
- What are your backup and disaster-recovery needs?
- Security! Security! Security! This is a sub-category of network design that is a specialized and complex topic of its own.