What is the best chain to put on our bikes? I like black, but something flashy might look good on my bike. The performance of the chain is more important to me than the looks though.

https://www.daidocorp.com/index.html
Anything that meets or exceeds the OEM. The OEM uses this brand. Probably this type of chain does not come with a link clip. It will take a special pin mushrooming tool, then measuring the crush does not exceed said measurement. Any farther causes pie cut cracks at the mushroom.

I read that the stock rear sprocket has 116 teeth. If I want to gear up to a 114 sprocket, the two teeth reduction would mean that I need a slightly smaller chain, right? How many links correspond to 2 teeth in the rear sprocket?

If you're goal is to make the bike a sport tourer you could consider going with the 40 tooth sprocket (vs. 42 stock) and actually leaving the chain a bit longer for a slightly longer wheel base. Not sure how it would play out but my guess is you'd still have room to tension the chain.

I would buy the stock size, and if you need to you can easily cut the links with a angle grinder or similar tool, if the need to remove links arises.

If you're just going to cruise the chain shouldn't stretch much anyway as long as you have good maintenance habits.

Using stock 118 link chain going from 17/42 to 17/40 will
increase the sprocket distance by .62"

Remove 2 links going to 116 links will make sprocket distance pretty much the same.

If you are worried about chain/sprocket wear the 17/40 is not
the best combination. Best wear is keep the keeping the most chain rotations to
match the same tooth at maximum to even the wear.

17/42 has same tooth/link every front/rear = 17/21 roatations
17/40 has same tooth/link every front/rear = 8/20 roatations

Check out https://www.gearingcommander.com/