Question: When I bought my baseboard heaters, thermostats and 220V breakers I was advised to get 12/3 wire. When I attempted to install the heaters I found that the thermostats, heaters, and even breakers have connections for only 2 wires. I have since read that 12/3 is only necessary for wiring something like a dryer that uses both 220V and 110V over the same wire. My question now is, should I get 12/2 instead of 12/3 to wire these heaters?

Answer: 
You should use 12/2 if the 240v appliance requires two hot plus ground. If you can't find 12/2 wire that has black/red/ground... you can use the more common wire that has black/white/ground where both black and white are hot. If doing this you MUST identify the white wire as hot at the appliance (or outlet if used) and at the panel. I always use colored heat shrink tubing because electrical tape almost always falls off after many years and is not reliable. Also make sure that you're using a proper 2-pole breaker at your electrical panel and if using an outlet, use the correct type to match the circuit's amp rating.

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I had a similar situation when I wanted to add 240V baseboard heaters to my attic renovation. I was initially told I needed to run 10/3 for a 240V line (I forget who, maybe my father-in-law or the guy at Home Depot), so I ran 10/3 from the basement through two stories and up into the attic. Later I found out all I needed was 2 conductors for the heaters so I ran the 10/3 into a junction box in an attic closet and then had 10/2 go from there to the heaters and thermostat. I put a wire nut on the unused conductor in the junction box as well as at the other end inside the electrical panel.

I wish I had known that I only needed 2 conductor when I was fishing it from the basement as it would have been easier to deal with and cheaper.

Where are you located? My experience is in the USA and I am NOT an electrician (though it did pass inspection from the city).