I am working on building my bike tool collection. There have been a few situations where I could have used a cone wrench. I looked up sets and most come with the following sizes, 13mm, 14mm, 15mm, 16mm, 17mm, 18mm and 19mm, so I assume these much be pretty common. I notice the also sell them 20mm+ as well. I am not mechanically inclined enough to just look at the part to determine what size I need so I cant just purchase an individual wrench. Thanks in advance for any replies.

[Caveat: most of my bikes are 70's-80's]. I use 13, 14, 15, 16 pretty regularly. Whenever I've needed a 17 or larger, it wasn't in a "cone wrench only" situation, so I could use a standard box/open end wrench. Offset cones in even smaller sizes can be handy to work on brake calipers, particularly older ones. That's on my list for future purchases.

I need to have 2 15s to do mine.

As ExPres notes, it depends on what you're working on. My stuff is Shimano within the last 15 years; the 13/15 mm wrenches work for the front, but the rear takes a 17.

If all else fails, take the bike - or just the wheel - to the LBS and figure out which size fits.

My various Shimano hubs and prebuilt wheels have required 13, 14 (2), 15 mm and 17 mm cone wrenches and a 17 mm ordinary box or open end. The two 14 mm were for a Dura Ace hub that had locknuts that needed a cone wrench. I have never seen anything that needed an 18 or a 20 mm cone wrench.

+1

Bicycle Research made a cone wrench , double stepped , double ended..
so 13,14 on one end, 15,16 on the other.
so, you just need 2 ..
As said, a 17 may be used for locknuts,
but a common wrench would take care of that

I've got these:
https://www.performancebike.com/bikes...8_20000_400148
and they work fine. Only problem I've encountered is with hubs that have over tightened lock nuts. In those cases, I just put wrenches on the two lock nuts to break them free then proceed with the service.

I just lubed and adjusted the Ultegra 6700 hubs on a new wheelset. The front cones were 13mm, rear 15mm. Both the front and rear lock-nuts were 14mm and required a cone wrench as well (regular wrench did not fit).

My Shimano WH-R560 prebuilt wheels require a 17 mm cone wrench for the front wheel's locknuts but can use a regular 17 mm open end for the rear. Strange.

My LBS told me that BMX bikes uses 20mm and 24mm cone wrenches for the rear 9 tooth hub. Unless it was 24 and 28.