Just run the wire size calculation
300ft is no problem you have to use the calculator and up size the wire to cut the voltage drop.
Here is one that I like
Wire Size Calculator
tom
RxRatedZ71,
I used the Wire Size Calculator that Tom gave the link to.
Load Calculation
Overhead lights 15 A
Refrigerator circuit 15 A
Space heater circuit 15 A
Circuit for other outlet 15 A.
Total: 60 A at 120V
Solution
You could run a 240 V line (3 conductors plus ground) to your barn from a 30 A 240V breaker in your house panel. The 240V line will actually provide you two 120V lines at 30 A each for a total of 60 A at 120V which is what you need. Put the refrigerator circuit and space heater circuits on opposite 120V legs of the 240V wire to balance your load and to minimize voltage drop. Using the online wire calculator:
120V, 30A, copper, single phase, 265'
Wire Size
You need a #2 size copper line between the house and your barn and you will be fine. If you go with a smaller wire, you will have voltage drop problems at the barn which will cause problems and could damage your equipment (especially the compressor used by the refrigerator). This design does not require an extra meter as you requested. However, doing it this way will have an up-front cost of paying for the large #2 wire.
If you were willing to pay for the extra power company meter at the barn, then you could run a much smaller wire (less cost) to the barn because you would be running a high voltage line which would be stepped down to 240V/120V using a transformer close to the barn.
Note: I have an electrical engineering degree but am not a licensed electrician so get a professional opinion before proceeding.
Good luck with your project,
Obed