Will my tap water work for brewing espresso? I just picked up a Gaggia Classic and I am wondering if my delicious Denver tap water will do the trick or if I should go with something bottled. I am looking here for the espresso standards and here for the Denver water report. 

Nearest I can tell, it's pretty close to the sweet spot for total dissolved solids but I don't know how to decipher the other values like pH. 

I plan to descale every now and again so mostly I am just curious if this H2O will cause any serious pain.
Provided that you descale your machine whenever needed, your machine should not take damage from using tap water.

Since your tap water is also safe to drink, this leaves taste as the only reason for concern. Dealing with this question is simple: just make a direct comparison between bottled-water espresso and tap water espresso. Check if you taste any noticeable differences. If this is not the case, the tap water should be fine. While there may be "guidelines for taste" as far as the tap water vs. bottled water question is concerned (e.g., softer water is typically better), what tastes good and what does not is a very complex question - so the tasting is the only way to be sure.

Note that you will need to descale your machine from time to time in both cases - so using bottled water to avoid descaling is probably not cost-effective (nor environmental friendly).