To chime in on the electricity costs since I work at an electric cooperative...heating/cooling are by far the highest user of electricity in the home. Changing the temperature to different settings throughout the day will be a big reason for higher kWh consumption on your bill. Because the outdoor temperature has such a high impact on how hard your unit has to work to regulate temperature, keeping it set on one consistent temp should actually save you some money on your bill. It seems counter-intuitive, but changing the temp on your thermostat multiple times per day is one of the worst things you can do if you're concerned about saving money on electricity. Also, with a home built in the 1960s I would immediately assume that the insulation is probably costing you money on your electric bill also. People lose so much hot/cool air through poor insulation, and can't figure out why tampering with the thermostat isn't resulting in more savings.
From a "how the bill is structured" perspective, utilities have shifted over the past 10 years regarding how they recover costs. Many used to focus on keeping fixed charges as low as possible; which meant recovering costs through the kWh charge. This meant that utilities were "chasing" cost recovery many times and potentially having to raise/lower the kWh charge many times in a given fiscal year. Now, many of them have figured out that it's much more financially sound to increase fixed charges to recover costs (purchased power, infrastructure maintenance, etc.) in order to reduce the wild swings in rates/bills that are caused by weather volatility. That has made the actual sale of electricity pretty much a straight pass-through from the power provider to the customer...with utilities not making a dime on actual electric sales. Bottom line is that in order to save on electric bills in today's world, you'd need to consider upgrading things like insulation, windows, sealants, etc. Energy efficient appliances, LED bulbs, using power in off-peak times, etc. are good ways to impact your bill...but if you really want to get some bang for your buck, upgrade the shell of your home.
One other (admittedly potentially very expensive) option would be to look into a solar installation. We have members in our coop who invested in solar through a TVA incentive program, and many months those people end up with a credit instead of owing anything on their utility bills. I haven't looked into it in several years, but the initial investment to payoff break-even point was terribly long (maybe 20 years)...but if those costs have come down significantly, it could be worth looking into.