You have a difficult question to answer, since in many cases you always learn with any job after you get it. :)
"No experience required" are jobs that an employer thinks they can teach quickly while you are doing useful work. Jobs like dish washing, fast food, and cleaning can be like this... you can starting doing something useful in a matter of minutes. But getting REALLY GOOD at the job may take a while (watch some of the "Under Cover Boss" episodes where the CEO has trouble keeping up making burgers during lunch rush!). You often get out of the job what you put into the job.
To me... any job experience helps show you are ready for another job. You had to get up, make it to work, interact with a boss, accomplish some task, and collect a paycheck while continuing to live your life. This always counts, regardless of what you are doing.
You mention in the topics that you have "computer software", "management" and "lead" in mind. While it is not impossible to move from "no experience" to "software developer", I have heard the "rule of thumb" that "1 year of college is worth about 4 years of "real world" experience". That makes sense to me since you get a LOT of information in college and can focus on both learning... and learning how to learn quickly. Not fun, easy, or cheap... but does provide you with skills an employer will want.
Everyone has different situations, and you need to do what you can. College or other training is required for a lot of jobs since the businesses need the help NOW, and don't have the time to help with the training. "Entry level" and working your way up is possible.... but probably harder in the long run that getting the training for the job you want.
Best of luck!