Many of the RBOCs (if they can be called that anymore) use the Common Language Circuit Identifier (CLCI) nomenclature for identifying circuits.
Many large carriers, especially those that have spent more time buying up competitors then integrating previous acquisitions' provisioning systems, have a mish-mash of different circuit numbering schemes, depending on whose underlying plant and provisioning systems were used to build the circuit in the first place.
Like you, I have seen everything from telcos that just use a number and not much else, to telcos that try to tell someone's life story in the form of a circuit ID, to forms that are somewhere in between. I won't say one is better than another, but I do favor shorter ones, if for no other reason than they're easier to key into provisioning systems, interface desciptions and put on wire labels 
I also got into the habit a long time ago of recording every circuit ID for a particular circuit. Many of the circuit I dealt with were long-haul circuits, or were provisioned by a LEC and had to be handed off to an incumbent carrier for final delivery to the customer, and one particular LEC burned me several times by stating, "Oh, I see we hand that off to $TELCO... I don't have a circuit ID for that piece....".
Since you have the luxury of starting from scratch, you have the option of creating a system that best fits your needs. If you have or can build a provisioning system that captures all of the information you need, then you can get away with a simpler ID, such as a plain number. The information you want to capture would depend on the type of circuit, but would generally include things like carrier/customer handoff points, router interface/switch ports, VLANs, MPLS labels, patch assignments, etc...
It's also a good idea to come up with a standard format for identifying your facilities/rooms/racks if you haven't already. Many providers use Common Language Location Identifier (CLLI) codes for this, which is another telco hold-over, but you can ID them however you want, as long as it makes sense to you and scales as you grow your network.
jms
