Get a good domain name.

Use your web host not jufst for the web site, but try to utilize functions for office automation. 

There is no reason to use the internet service provider  as your main email address and NOT use the one from the web site. (Surprisingly enough MANY do this).

Find a web host with rich features and plenty of resources to give out -- such as mail space, disk space, bandwidth, tools, etc.

Use other programs, in addition to web site, such as forums and blogs.

For new software solution requirements for your company look for potential ones that are web-enabled. (Do not use outdated technologies, if possible).  If you are in doubt, do hire an independent software consultant (such as IstoThalassa), sacrifice a small fee, and sleep quiet for the next few years.

Using web-enabled technologies may potentially mean replacing the local area network server with the internet provider and web host infrastructure -- In this way you will avoid the burden to maintain a local server, manage local databases and do local backups.  Instead all these will happen at the web hosting provider premises saving you resources: money and time.  And of course the accessibility will be improved as well as the up-time.  This is especially beneficial if your organization is distributed in more than one geographic location (different offices, cities, even countries).

Additional benefits include you able to access the web software during traveling or via your web enabled mobile phone.

Look into using some freely available tools and software -- yes, sometimes these are better than the paid ones.  Do not hesitate to pay for professional help to dig them out.  For example use Google Calendar, open source forum software, open source content management, open office, etc.