Well it sounds like having the most puncture resistant tires isnt a necessity since you haven’t had issues with the road tires your using now.

You will feel a difference in a heavier tire but if your mainly doing a 14mi commute everyday, I wouldn’t worry about it. On a century/longer ride a flat will cost you much more time than some added weight/risistance. If you have wheels on the heavier side the percent of added weight from the tire isnt as noticeable as if you are running light wheels with heavy tires.

Depends on the group ride Id guess. I train on 25c heavy tires on my road or cross bike for everything minus road races. Ive never thought that a wider, slightly heavier tire was an issue as long as your legs are as strong as everyone elses out there. Then when you go down to 23c light, sticky tires, youll feel faster

Id say it sounds like your looking for a more fast than puncture or comfort. The gatorskins are pretty good, though ive had more than a few fail due to sidewall issues. Everyone has opinions on what tire they like and why but youll really have to order some and test them yourself. Personally for the price/puncture resistance I like the freedom thickslick.