I am looking to upgrade parts on my Rocky Mountain Metropolis bicycle and want to go to SRAM products. Since I ride my bike everyday, I want the best SRAM parts. Looking at the Red line. That being said, I like the frame and handlebar configuration on my bike. I need 2x10 speed shifters. Thinking about getting the SRAM SL-700 10 speed trigger shifters to work with the SRAM Red 10 speed front and rear deraileurs. Will that combination work? Is there a better option?
The SRAM road derailleurs and road shifters you've selected should work together.
However, the bigger problem might be that you need a 10 speed cassette (for which you'd have to look up the hub to see if its 10 speed ready). It seems like the 2015 YVR model has a 10 speed compatible hub, but check yours. If you don't have a 10 speed ready hub, you'll probably want to get a new rear wheel.
You also need to make sure the SRAM FD/RD can shift your chosen chainrings + cassette.
As for buying the best parts, note that the more you spend, there are diminishing returns, and you can get excellent shifting with well below Red 10 -- e.g. with Apex or similar. It doesn't really make sense to equip a cheaper bike like the one you have with top of the line components, especially since you probably wouldn't notice the difference from a lower end group. You can also get a mountain RD since the cable pull is the same and save some more money. I personally wouldn't go up to the Red level on this. Also, ask yourself if you really need 10 speed -- 8 or 9 speed is cheaper to run (chains, cassettes) and buy, especially if you rack up a lot of miles.
And you're upgrades cost close to what the bike is worth or more, so you may want to just sell the bike and get another one with higher end parts.