Common protocols include ftp and ssh. ftp is fine if you just need to access your files.
Is the work computer behind a firewall? Just ping the IP from home to verify.
For the home computer, do you have a static IP or DHCP (from the ISP)? Most are DHCP, which means that the IP can change on different logins. This makes it difficult to connect to it from outside. To try it, turn on DMZ (in the router configuration) and try pinging from work.