You should do the crank swap and the installation of the Mountain Tamer at the same time.
If you do the crank swap before you get the Mountain Tamer you might end up having to replace the bottom bracket with a wider bottom bracket when you go to install the Mountain Tamer.
I assume you are not going to be doing this work yourself since you are new to bikes.
You are also going to have to replace the front derailleur with one compatible with a 44/32/22 crank.
Mountain Tamers may not work with integrated cranks. A splined or a square taper bottom bracket is more likely to work because they are available in different widths. So, the replacement crank that you buy should be compatible with a splined or a square taper bottom bracket.
If you do the Mountain Tamer you'll have to run the front shifter in the friction mode. In other words, there will be no clicks, you'll have to guesstimate when making a shift. There's nothing wrong with this. You would get the hang of it.
Another alternative is to go to a bike with 26" wheels rather than the 700c wheels of the Trek 520, like the REI Novara Safari. 26" wheels give substantially lower gearing. The Safari comes with a 48/36/26 crank which could be swapped with a 44/32/22. The front derailleur would not have to be replaced in this instance.