To answer the question, a T1 typically is nothing more than two copper pairs which are converted from analog to digital, with special conditioning (and signal repeaters if the distance requires them). If your location could get two additional regular phone lines, then you could probably get a T1 circuit without additional construction or trenching. If such additional work would be necessary, it's quite possible that you would not be charged for that work. In our industry, special construction costs are identified after the order is placed, and the customer can cancel the order with no penalty if the additional costs are not acceptable. It's not likely that construction costs can be identified prior to an order.
Most responsible internet providers will give you a dedicated internet connection at the full 1.5M speed. There are local "tier 2" providers that will purchase a certain bandwidth from an "upstream" provider, then resell it and oversell it. For instance, "Joe's Telecom" might buy a 45M DS-3 of internet access from AT&T. A DS-3 has enough bandwidth to support 28 T1 circuits. Joe will recognize that not every one of his customers will be using the full 1.5M at all times, so he will sell more than 28 T1 circuits -- this is overselling. So long as he watches his circuit utilization, and orders more bandwidth before the customers start crashing into each other, then all is well. But if he's like Comcast, and severely oversells, then customers' circuit performance will suffer. So you will want to know if your T1 circuit is dedicated access all the way to the internet backbone, or if it goes to Joe's concentrator where it is shared among his customers. If the service you get is from AT&T, Sprint, Verizon Business, Global Crossing, Qwest, Savvis, Internap, Level 3 and a few others, then you're dedicated. If it's from a local provider with a limited service area, it's probably shared bandwidth, and the pricing should be lower than from a dedicated provider. But....the quality defined by a Service Level Agreement (SLA) and QoS (Quality of Service) will also be lower.
Relative to a router, in your quote requests mention that you want "managed" service, which tells telecom companies that you want the T1 router to be included as part of their package. The T1 router is different than a typical "broadband" router one would get at a local electronics shop. T1 routers have built-in CSU/DSU functionality which assists in the synch up of the circuit. Some typical T1 routers are Cisco 1841 and Siemens 5940.
A free quote source highly recommended for fast, quality, personal service can be found at DS3-Bandwidth.com (they can assist with more than simple T1 if needed). Word of advice.....you must provide accurate contact information (installation address, email, phone number) and sufficient detail on your network requirements/application.....otherwise they'll ignore you as a bogus request. If you're serious take advantage of what they offer. If you're not serious.....go elsewhere.