You've probably already gotten new tires, but just for info in that case...Compass tires are now called Rene Herse tires. Same tires, different name. Each different size and model of tire comes with a unique name, which can be confusing. They also almost all come in different casing configurations- standard, extra light, endurance, endurance plus. I've used the standard and the extra light, and I like the standard a lot.
Re the Advent X stuff... I've heard good things about it, too. At $250, the price seems decent for what you get, too. However, in your situation, there are at least three things you could do. One would be to spring for the Advent X parts with a new chain and the required tools. Another way to go would be to just replace the chain and cassette. Assuming your current bike is nine-speed, you're looking at around $35 for a Sram PG950 11-34, or $20-something for a lower-end Shimano, or, if your derailer will do it (it probably won't) $35 for the Microshift 9-speed in 11-42. Plus $20 or so for a chain.
And then the third way you might approach it would be to just get the Advent X rear derailer, cassette, and shifter, plus a compatible chain. You could use your existing crank, remove the front shifter and just use the limit screws to align the front derailer properly on the middle ring.
I'd be inclined just to replace the cassette and chain only. I like the cheap stuff, especially chains, because then you aren't so reluctant to replace them regularly, which then helps your expensive stuff like chainrings last a long time.