Firewall is used to protect internal IT infrastructure from being attacked from the internet. Cisco Pix or software solutions like Checkpoint and Microsoft ISA are firewall products and widely used today to protect internal IT infrastructure from Hackers.
Proxy Servers are used today for sharing the internet connections and protecting internal user information like IP address from the internet. Internal users in the company can access the internet with the same connection using the proxy server.
Typically cyber café owners and similar sized setups use proxies. Proxy servers work under application layer and firewall works under networking layer.