What your company need is a VPN (Virtual Private Network). Using such a system I can access everything within my company whether I am at home, in a hotel, or office abroad. It is a little slower to move emails to the archive, but I tend to store items in local folders on a temporary basis. Opening emails from archives or documents from the network is not significantly slower than working from the office.

You certainly do not need a dedicated server. Some companies will only allow VPN access from their own machines (which they know have anti-virus software) as access from other machines could spread viruses. However, I also use a web-based access method which is not proper VPN and this works faster than VPN, but has limited access to resources.