Some networks have outgoing connections to port 25 filtered. This is extremely bad, as it removes the ability for M3 to automatically fail over to other MX hosts. If there is any possibility of removing the outgoing SMTP filter, that should be your primary target.
Email is, in itself, extremely fault tolerant, and the protocol itself is built around the ability of multiple hosts to receive and deliver mail to a single target. By filtering this, your network is removing a large part of the redundant alerting capability of your M3 server.
If you network can not have outgoing SMTP filtering disabled, you should investigate in moving your M3 server to an unfiltered network, such as provided by the M3 Hosting Partners.
We do recognise that this may be infeasible for some clients, and we've added a fall-back SMTP relay option. This is available in the 'Settings' page, and on the first 'Install page'.
Most of the time, if your ISP has provided you with a fallback option, entering that into the 'Smart Host' setting will be sufficient, you will not need to enter the Port or username/password.
Note that M3 will try, by default, to use fully encrypted communications by default (TLS and SSL) before falling back to un-encrypted.
The same options are available on the Settings page, under the Email tab.