You have a couple different options. I think the cheapest would be to switch to a compact crankset which would change the front chainrings from 52-39 to 50-34. I'm pretty sure you could do this while still using the same shifter. Changing the front shifter is required if you want to go from a double to a triple, as is changing the front derailleur. If you switch to a compact I'm pretty sure you can keep the same derailleur and shifter.
Another thing you'll want to look out for is the rear derailleur. You currently have a short cage derailleur, and you may need a medium or long cage derailleur when you go with a compact crankset.
I don't think a triple should really be necessary on a 10 speed system. I have triple, but I have an 8 speed cassette. I find in that case the triple is nice because you can still get lots of gear range while still keeping the gears close together, However, on a 10 or 11 speed cassette, this isn't really necessary. I think that switch to a compact crankset is a much better option.
Also, according to This post, the maximum cog size of a short cage Shimano short cage is 27 and the total drivetrain capacity is 29. To use a larger cassette, you would have to switch out the rear derailleur. If you used a compact crankset, you should be probably also replace your rear derailler for a medium cage, as your total capacity would be (50-34) + (27-12) = 31. However, if you changed the cassette to a 12-25, you could get away with not replacing the rear derailleur and still getting a little bit lower gearing, although possibly not enough for your needs.