Upgrading a Specialized Sirrus 2015? Not having biked since I was a kid I went ahead and bought a Sirrus 2015 (the base model) for commuting 2x a week (~100 km weekly total) with a view to do 3-5 days. I've done about 1000km on it so far. I'm a fairly heavy guy at (210 lbs but fit from running/lifting) and commute with a backpack. I like the frame, seat and flat bar, but the shifting is slow and imprecise, and I've had it back to the shop a few times now for clunking and clicking in the bottom bracket/crank area. This issue just recently seemed to reoccur. So I'm concerned for the longevity and quality of those components. I've broken the stock pedals too.

Should I be upgrading my components? (I would be willing to shell out about $500 or so) What should I target for the budget?
Yes, my friend just bought that bike new and ended up taking it back and getting a similar priced Cannondale, mainly because it came with a Shimano 105 group set. I would look at that as a major upgrade especially if you are experiencing poor shifting. If you have 500 to spend you could probably get an Ultegra group as an even better upgrade and have a really nice performing bike on your hands, as well as lighter. I'm not partial to Shimano so I'd probably check out Sram as well, Rival will be in your price range. 

A new wheel set would be the other major upgrade you could make for 500. There are a ton out there at that price but if shifting is what's bothering you I'd get that taken care of first.