Enohabam,
So, the company you work for is trying to get into the Telecom business; good luck. It used to be that you could go to college and learn everything there was to know about Telephony, but that is not the case anymore. The majority of the information is tied up in old guys like myself and others in older companies that have been around for a minute; like DND ON.
As for deploying the equipment in various locations and using different trunk types the answer is yes and no. The issue you are running into is with an Analog Trunk line which isn't really used anymore by medium to large customers except for 911 services and even that is rare. Even using Analog services going forward will require you to connect to a SIP Gateway that provides the Analog service. This means it will most likely be more controlled since the last mile now becomes the last 3 feet. For the most part you typically won't have any issues with integrating with whatever physical trunking service you go with. The issues you will have will be with SIP trunking and other applications that the customer wants to integrate into their existing services.
As for which equipment you are going to partner with that is up to the owner of the company and what they believe they can sell in your market area and target audience. The top 3 systems in the world now are Avaya, Cisco and Mitel, but that also comes with a hefty price as well. The Digium system is branded Asterisk PBX that has support through the Digium provider, but I don't believe that it can be used as an Enterprise solution. As far as NEC goes it has been around for awhile, but it is not a big player within the US anymore as far as I can tell; maybe it is in Canada.
Thanks,
TE