Yes, IVM would be a good solution for your set up.
VoIP technology would be recommended. Instead of your phone-lines coming into the computer through a voice modem (which may reduce the call quality or have other difficulties such as detecting Caller ID, the end of a call, the digits users press on their phone's keypad etc.), VoIP lines are entirely digital and work over your broadband internet connection. When a call comes in, it rings your computer (or IVM) digitally from the internet, and sends the call over. The caller on the other end will not know the difference from a normal analogue line and the VoIP line answering the call, but on your end it can make the world of a difference. You can also hook up a normal telephone to your VoIP lines using an ATA adapter, or purchase an S/IP or USB digital VoIP phone.
The other advantage of using VoIP is that some service providers allow more than one incoming call at the same time, meaning multiple lines are unnecessary. (Note only some VoIP providers allow multiple communication channels). A further advantage of using VoIP is that it is much cheaper than your standard land-line phone system. For example some VoIP service providers have plans for free unlimited/untimed phone calls to anywhere in the US & Canada for a low monthly price in the $20/mo range.