I recently bought an inexpensive, '90's mtb to use as a commuter, and went through a similar process. My use case is different (100% road riding), but I was faced with the same dilemma of looking at tires that cost more than the bike. As much as I would have loved to put Rat Trap Pass tires on the bike, I couldn't justify them based on the use. I ended up getting a pair of one of the Schwalbe 26" tire models from our friends at Bike Tires Direct (I think they're the Big Apples--an advantage of those for my use is that they have a reflective band). They are anything but supple, but they are fine for what I need.
In your case, I would still be hesitant to spend $170+ on tires for a $25 bike. Compass tires are awesome (I have the Bon Jon Pass and Babyshoe Pass tires on different bikes), but if you're looking for tires for an "end-of-the-world bike" that's suitable for singletrack, some of the more durable/less plush/less expensive options with more tracktion are probably a better fit. Bike Tires Direct actually has a pretty good selection of slick/semi-slick 26" tires.
https://www.biketiresdirect.com/sear...&fcat=csl&so=b