There are many inspections that can be done as a function of buying a house, but be sure that they are included as contingencies in your standard "purchase and sales" document when you make an offer. Because every house is different, you will want to have experts in your corner when you are considering becoming the owner of a house, new or old.
The traditional home inspector will review the structure, roof, electric and plumbing systems, look for anomalies in the heat and air conditioning, and will likely mention if he saw evidence of any pests. But if you want a termite inspection that will be a different inspector. Ditto chimney and details on a furnace and A/C. If there is a swimming pool, or solar panels, probably you will have different inspectors for them, and if you want to check mold--that might be a different inspector as well.
Meaning, if you have every inspection--you will be paying more than your lunch money for the results.
Probably you should start out with a good solid local home inspector. Follow him around as he does the inspection. Ask questions and keep a good dialogue going as the home reveals itself to you. You will get a sense if or why any other inspections are suggested, and can then make up your mind. You will see the strengths and weaknesses of the house and the inspector will give you a good sense of the quality and what you are getting for your money.
If you are spending all your "extra" money on this home, ask the seller to include a home warranty as a part of your offer. That will cover all the appliances, the AC and Heat, the electric system and plumbing. There are a dozen or so of these companies, they are a form of insurance and so they must be approved by the NH Insurance Commission--so you can research them via the commission. The warranty will fix or replace anything that goes wrong during the 1st year.
Hope this helps,
NH and FL Real Estate Professional