Cost of doing 1" vs. 3/4" while you are replacing it anyway will not be much higher. I have 1.25" for the main line coming from the meter, then down to 3/4" partway through the crawlspace and running to all of the destinations. The actual connection to my 120k BTU furnace is 1/2", as are the ones to my (old fashioned tank )water heaters. While the walls were out, I stubbed out gas to the range location, even though I'm installing induction. Cost little, and I like to keep options open.

If you figure 1CF of gas per hour as equal to about 1000 BTU/h then you would need a 1" main to serve your house and a 3/4" branch to serve both the water heater and a 120,000BTU/h furnace. The range can be served by a 1/2" branch. This presumes natural gas at low pressure and using schedule 40 black iron pipe.

First off, the inspector is not completely right. Grounding and Bonding is one of the more involved sections of the electrical code. Things like gas piping don't get "grounded" they get "bonded." The meter itself isn't required to be grounded or bonded. The question is whether the interior gas piping should be bonded. Gas piping is only required to be bonded if it is "likely to become energized." That determination is made by the local jurisdiction providing the permits/inspections NOT some presale home inspector who lacks any credentials for making that determination. Your best bet would be to make an inquiry to the local jurisdiction if you want the true answer though sometimes the local gas company will be more responsive in guidance.

@ramona1976 is right, the BTU load has to be calculated for each section and sized accordingly. That's not possible with the info given. Here's an off-topic opinion though: You are building a new house in the South East US. I'm guessing an a rural area based on the lack of NG and the barn. I'd diversify energy sources, put a lot more emphasis on solar PV and dial waaay back on the propane. This house is going to be around for 100 years or more. Build it for the next 100 years, not on ideas from 60 years ago. Start with a hybrid heat pump water heater, and heat pump for the main house. Maybe a heat pump for the barn as well. Keep the propane for the generator, gas logs and stove if you want. Put panels up to supply much of your electrical needs. Propane is expensive - and it's been unavailable before. Don't put yourself in that position.