13-14-15-17-19-21-23-26

There's no 16 or 18 cog. Most road riders want a 16 because the jump from 17 to 15 is big and there are situations where the 15 is too hard and the 17 spins too fast. Some like an 18 cog too although some think it feels about the same as the 17 and 19 next to it.

Pushing on the pedals too hard and pedaling slow can be be very fatiguing - _Training and Racing With a Power Meter_ has an anecdote about a rider who got dropped every time he spent five minutes pedaling below 70 RPM at an intensity he could otherwise handle for an hour. It's hard on your knees. If that happens switch to a bigger cog. When you run out of cogs switch to a smaller ring noting that's a very significant change - with 42 x 26 about the same gear as 30 x 19 (this is a simple ratio - 26 / 42 * 30 = 18.6 which is closest to 19) moving directly to the 30 ring without a cog change too is three gears easier which is a bit much. Because of that many people like to change the rear derailleur at the same time as the front - I'd move two cogs smaller at the same time to end up in 30x21.

You can also pedal too fast for comfort. This is trainable and something you want to work on because it's good for endurance, speed, and can make for less shifting but there are still limits. Moving between rings is also a big jump, with 42 x 13 nearly identical to 52 x 16. The next gear there is 52 x 15.

52 x 26 and 30 x 13 should be avoided (they may not be quiet).

Shift to the 30 ring and 21 cog. You're not going to stress anything.

If you don't need 30x26 you want a 13-23 which adds the 16 cog, and if you don't need 30x23 a 13-21 may be better (with the 18 cog too). If 42x26 was easy for you on the steepest hills you might run 53-39 (or 50-39) x 13-21 but it's not. Compacts are not a good idea unless you're a bike company (fewer SKUs means bigger profits) or have a lot of cogs. I rode 50-34 x 13-23 9 cogs (with the same range and spacing as 50-40-30 x 13-21 8 cogs plus the belief that two rings are better than three) and it was horrible - every time I dropped below 17 MPH I shifted five cogs from 50x21 to 34x15 and when I accelerated past 19 MPH it was five cogs back from 34x14 to 50x19 and instead of riding 40x17 or 40x16 in the middle of the cassette I spent a lot of time in 50x21 and 34x14 one cog in from the end which were noisier. 11 cogs in back would have restored the better shift pattern and chain line from the triple ( 46-36x12-13-14-15-16-17-18-19-21-23-25) although an 11 speed cassette and chain can cost more than some bikes. I switched back to a triple when I moved on to 10 cogs.