Kotebiya, you explained your problem, but it is "so open" in a algorithmic context.
"Finding the best route" or "Pathfinding" is a Graph Theory (graph traversal) problem;
GIS is an "user of graph solutions", so, is not really a core-GIS problem.
Some of your inputs, for your pathfinding problem, can be from GIS, but, perhaps, not all. Let see your context-openness and some "accumulating factor" inputs:
it is a transport of goods or transport of people problem? There are different approachs and theories, see commuters flows for people (see @SharonB suggestion).
two metropolitan centers: it is a metropolis of a chaotic megacity (like São Paulo or Cairo) or organized "normal" city. The chaos produce very high stress coast in the case of people transportation.
road/rail/bus (and about bike?): for people transport, road have per km cost plus toll (plus stress), rail and bus have near fixed cost (minus subsidies plus departure tax...).
coast as time: energy consumption is near proportional to euclidean distance (easy measure with GIS), but "time with the engine running" may not be negligible... By other hand "time is money" for people transport: what people? what the average cost of hour of that people? It can be quite sensitive factor, changing all the weights of inputs.
sum of segments: your model have only "per segment" metrics, or can acount some "total distance" or "total time" approximating effects?
today or tomorrow: average traffic speeds, in the past years are much greater than the projection of the coming years. Your data must be corrected by this factor; by segment (near big metropolitan centers have less future speeds), by type (road/rail/bus), etc. if need more precision.
So, matrix-data and matrix-weight-factors for your "money cost of travel as a cost accumulator per segment" perhaps have more "external" information than information encoded in usual GIS maps.
Transportation networks digital services, perhaps have more data than your oficial metropolitan database. You need to dig by another sources. Example: Google Directions API or OpenStreetMap Routing... And check how to, in your segment analysis, add conditional factors, like toll prices, etc.
pgRouting tutorials, pgRouting articles (like this), and ArcGIS tutorials
are good starting points.
For scholarly analysis, the articles cited by @SharonB and @FManenti (a PDF from 2001 for classic analysis) also are good, but not show where is easy to dig information.
For general view of the "time is money" problem: see this good article of london.gov.
Another sugestion: not close your universe by ArcGis or ESRI solutions -- delete your Arqgis tag if you want the help of all people of this community. There are so many open source solutions. See also PostGIS (Topology module) and pgRouting solutions.