Adobe will sell you a license to use Photoshop CC 2014 and Lightroom for $10 a month, in their "photography" bundle. They have promised not to raise the price for a very long time.
https://creative.adobe.com/plans/photographyOr you can buy Photoshop Elements for $99 outright. I don't think there is anything in the video above that you couldn't do with Elements, but get the Free Trial version and test it out. The big difference with Elements vs CC is the addition of Smart Objects, which are very worthwhile to learn and use but a bit advanced for a beginner. (For instance, in the video above, if the L layer was first converted to a smart object, you could resize it over and over with Free Transform without the constant pixel degradation - in other words, the third time you resized it would be just like the first time. This is useful for changing your mind when doing layouts. To convert a layer to being smart, right click on it and say "Convert to Smart Object".)
If you are intending to letterpress and need the pixels to remain B&W only, I'm pretty sure running Minimum is anti-aliasing the image (zoom in and you will see gray values along the edges).
It should be noted that unless you are outputting to letterpress where the printer has asked for B&W pixels, you would be better off using Levels rather than Threshold. Adjust the middle control/gamma adjustment in Input Levels to the right and the mid-gray values will darken, but don't go all the way to the max. This will darken/thicken the lines and reduce the number of grays without removing the grays completely. Antialiasing is a good thing to increase smoothness if you have enough resolution (it might help to bump up your resolution - ask your printer as Photoshop's upscaling algorithms are pretty good these days).
gah.