Two isolated LAN’s with single DSL line

I have a single DSL Modem/router with wireless capability that is connected to an unmanaged switch. I have a 10 computer peer-to-peer network for the office that uses shared files on the various workstations. I also have five workstations that need Internet access but have to be isolated from the office files since the office files contain private data.

I considered using a wireless access point but now believe this will not isolate the two LAN’s. Will a managed switch give me what we need or is there another solution? We are a nonprofit organization with a very limited IT budget but I can get a CISCO 2960 switch donated if necessary.