How do I know if solar energy is competitive with other energy sources in my region? How do I predict the associated costs?

Excellent question. Solar energy (and renewable energy, in general) has become competitive in many markets around the world, including in some parts of the U.S. NREL has developed a website where you can check if solar energy is competitive in your area. Also, many installers will provide energy audits so you can know what to expect.

What are duck curves? What do ducks have to do with solar energy?

Source: http://2greenenergy.com/2015/04/14/demand-for-energy-storage-in-a-changing-world/

When do you need the most energy? You probably don't need much when you are sleeping (which is why many do laundry at night, it can be cheaper). You probably need more when you first get home from work or school, when you turn your air conditioner on (or turn it up, or even, naturally, as you get into the heat of the day). Solar cells produce most of their energy during the day when the sun is shining. Distributed systems like wind power also have this issue, although they produce the most energy at different times of day.
A duck curve shows the net electrical load as a function of time. This is used by utilities to determine how much additional power needs to be produced to meet demand. The "duck" shape is obtained because solar energy produces most of its energy during the day, reducing the net load.

Will solar energy ever make it? We've been funding research for ages. It won't ever pay off. Do you take me for a fool? Sure, it might work in sub-Saharan Africa and isolated islands, but never in the U.S.A.

I don't take you for a fool--I just want to show the bigger picture. So much gets buried in politics and This research and support is actually paying off. For example, Deutsche Bank recently released their analysis of the prospects of solar energy and found that it is already competative in many locations, including the U.S. They state that "unsubsidized costs of solar energy are [currently] 30 %-40 % below the retail price of electricity in many markets globally." You can see how these prices compare in the plot above. Even in the U.S., they find that solar energy is competitive in more than 14 states without additional subsidies. Planners have been increasingly turning to solar energy because the economics are starting to work out!