Pretty tough to answer without knowing how your new application was designed to work. I'd actually suggest reading it's documentation, or contacting it's author(s) to get this info.
At a guess, it might need some or all of the following:
80 HTTP (non-encrypted web)
443 HTTPS (SSL/TLS encrypted web)
25 SMTP (simple mail transfer protocol)
20 & 21 FTP (File transfer protocol)
22 SSH (Secure shell, also used for secure-copy and secure-ftp)
There obviously could be more than this, and/or your new app could be using non-standard ports for standard services (e.g. using 8080 for HTTP) - it'd be really hard to tell without documentation or the authors (or sniffing the network while the app is running).
The other question is, does the application expect you to have a VPN or some other secure tunnel in place over which it will work? If so, then you might need to get that set up, and it would then run everything over that tunnel. Again, the docs / authors could help if this turns out to be the case.
Hope this gets you started;
Wire