If you really want to help your client out you need to investigate pricing and do a comparison concerning installations costs, monthly reoccurring costs, bandwidth available and features.
The client also seems unclear what is meant by a server. Even in a peer to peer network [workgroup/homegroup] you have a central pc that houses the accounting program and may contain the central depository of work files. This is referred to as a server.
Certainly the POS system isn't the only system the client is running. if it is then perhaps internet access at each location and a hosted [cloud based] POS is the right choice.
Depending on your area and assuming low end price range you have the following options:
T1's which come in two flavors, P2P and Frame Relay
Now with cable and dsl you have internet. But now you need to tunnel securely through the internet which is when a vpn comes in.
VPN's come in a number of flavors but for your purposes you only have two
Site to Site vpn.
You can't tie a POS system together over a client vpn. So you would need a central site that the other two sites connect to via site to site vpns. This means you have to have vpn site to site routers [don't confuse a vpn pass through router with this type of router] at each site.
Compare this to a frame relay network which requires a FR router at each site but connects all sites together though two sites would be routed through the main site. Something goes wrong you have technical support to call.
Really need to start with a needs / usage analysis. Those results will guide to what system/setup is best for the client.