To see which providers are in your town, check out the provider map from the NH Broadband Mapping and Planning Program. For example, Alton can be found at the link:
iwantbroadbandnh.org/townprofile/alton
DSL used to be a pretty bad choice if you have multiple heavy users in the house, but Fairpoint has been upgrading its service recently. Many areas in the lakes region are now able to get up to 15 Mbps, but the actual rate depends on the distance from remote head-end (where the fiber stops and the copper begins), as before.
When it comes to the cable monopoly, a Selectboard has no power to change providers. They can refuse to renew the contract for television service, but then they would have to find a buyer for the cable plant, or just operate without a contract. It is unlikely that Comcast would buy it! A town sponsored ultra-speed fixed wireless service would be an alternate answer, but it is unlikely we will see that soon. There is little demand, or free enterprise would have already given us alternatives. Perhaps our forum member "wifi" could weigh in on that issue.
Unfortunately, while the internet provides the technology to replace over the air or Cable TV, it will be years before the most popular content (like NFL or HBO) is available to those without a cable TV contract. It is a money issue. The mechanism that shifts the money you spend on TV to what you watch over the internet is the bottleneck. Carriers and content are splitting, and there is little money in neutral bitbanging (transport). Netflix, Hulu and the like are just the beginning of the next battle.