What you are in effect looking for is an IP phone system… there are lots out there. Asterisk is an Opensource version but does require a bit of learning. Most of the others are made and sold as ‘appliances’ by companies such as Cisco, Panasonic, Avaya etc. You can also buy pre-configured Asterix solutions.
I’ve put quite a few of these in for customers (run a IT/telecoms company – mainly Cisco in the past). You can get refurbished units now that are reasonably cheap. There are some that have a decent web interface which makes configuration/administration easier, but most do require some half decent knowledge of networking/telecoms etc. for you to install them yourself.
The other alternative, if you don’t want to get your hands too dirty, would be to get someone to do the initial build for you and then hand over with a bit of training so that you could look after it from there?
Alternatively ditch the PSTN lines and just buy a VOIP service from a provider and leave it up to them?
Depends on what you are trying to achieve, how many users, what you want to spend etc. etc.