What is the most energy efficient way to run an A/C unit?

Question

I recently installed a 12,000 BTU Mini-Split A/C unit with an inverter - http://www.tempstar.com/products/dfac.html

I was told that it uses approximately 0.6Kw/hour.

What I am really curious about is, what is the most energy efficient (to get the lowest utility bill) way to use this unit in various cooling scenarios, considering that I have a fan (60w/hr) in the room also. Basically when I am sleeping for a short period (say a 2-hr nap) or a long period (8 - 10 hr nights).

Say, it is in the day, and I want to take a nap in the room. Also assume that it is hot outside (90F). Should I just turn it on and leave it on for the entire time I am napping, or should I turn it on for a short time (say 30 mins - 1 hour), cool down the room and then use the fan, or some combination of the two?
In the nights, when we are sleeping for 8 - 10 hours.
When I am sleeping in the day for 8 - 10 hours, and it is hotter outside.

I know with some appliances, it takes a lot of energy to warm-up/turn on the unit than it does to keep it running for say a 30-minute or a 1-hour period. This used to be an issue with Power Supply Units, CPUs, etc. in computers back in the day. Is this still an issue today?

Is it an issue for my A/C unit?

If so, what's the most energy efficient strategy for getting the best bang (longer cool time) for my buck (lower utility bill), considering the above scenarios.

Thanks.

Does it have a thermostat that automatically turns it on and off depending on the ambient temperature in the room? — Ernie, Aug 02 '15 at 18:34
It has a thermostat, and I guess when I set it to auto it turns it on and off. — marcamillion, Aug 02 '15 at 19:01
You might find my answer to this question helpful: http://physics.stackexchange.com/a/189218/82798 — Daniel Griscom, Aug 02 '15 at 21:01
BTW, kilowatts is an "energy per time" value, so it makes no sense to say "0.6kW/hour". I expect the unit uses 0.6kW whenever it's on. — Daniel Griscom, Aug 02 '15 at 21:19
@DanielGriscom My apologies re: the terminology butchery. So if it uses 0.6kW whenever it is on, how much total energy (KwH per my utility) will it burn per hour? How do I figure that out? — marcamillion, Aug 08 '15 at 07:14
Simple: 0.6kW for one hour is 0.6kWh, and that's what you get billed for. (You might want to edit your question to correct it.) — Daniel Griscom, Aug 08 '15 at 11:46

What is the most energy efficient way to run an A/C unit?

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