So should I make my game an .exe or a .jar file? and do a lot of people have JRE on their PC
As a Java dev for a decade, I'd highly recommend you package it with something like Launch4J, so you can not only guarantee the JRE's inclusion, but the version you're testing on as well.
(for Mac users, every Mac ships with a JRE, very few percentage of users know how to launch a JAR)
Thankyou