Always try to get an idea of the fuel costs for any building before purchase. Request copies of the fuel bills from the owners and if they don’t have such records, request that thay call their fuel supplier and get a statement.
Most homes are heated with oil or propane or use wood. Natural gas isn't very common, but it is available in some areas (major cities like Concord and Manchester, and some smaller towns/cities along the pipeline.) Some few houses use electric heating here, but it is an expensive proposition due to electricity costs, and should generally be avoided unless you plan to replace it with a fuel-based heating source after purchase.
Any fuel-burning appliance should be serviced yearly (with the exception of very few space-heaters that get serviced every two years) by a reputable service company. New Hampshire does not license oil or wood-heating service companies. Gas-heating licenses have recently been created, but reports from those who have taken the training course seem to indicate that it is more of an exercise in memorization than of testing skill. Once you move, ask your neighbors who they rely on and if they are happy with the service they have received - it gives you a convenient excuse to introduce yourself, and while you are there you can ask for any recommendations for electricians, plumbers, auto repair shops, and other skilled tradespersons.
If you will be having major work done, make sure to ask for proof of insurance. Follow-up by calling the insurance company to verify, since a few unscrupulous individuals will obtain insurance coverage, then cancel the day after they receive the certificate. Five hundred thousand dollars is bare-minimum liability insurance, and most reputable companies will have one million. Some companies (particularly those that deal with commercial accounts) may have two million or even more.
Another thing to keep in mind when dealing with skilled trades is that they are often willing to accept barter in exchange for work. I know a plumber who replaced a water heater in a restaurant in exchange for fee meals there. Others may be interested in trading work-for-work, if you have a skill that they need (eg, computer repair, or landscaping). It doesn’t hurt to ask, although the larger companies are less likely to be interested, and the smaller shops are rarely not interested in some level of barter (of course, you might not have anything they want).