I think a lot of us get caught up in the numbers game, I'm sure more than a few have had go to, never miss guns they loved, until they got a chrony. Suddenly, that wonder gun is a weak sister, and they're trying to figure out how to get another 100 fps out of it :-).
That said, the chronograph is an integral part of our little game here, and for some, i.e. Talon shooters like me, they're just about required for getting these things dialed in. Springers not so much, although I had an issue with my first CFX, wildly varying velocities, that took a chrony to zero in on. All I knew for sure without the chrony was that my accuracy sucked! Besides, at the risk of sounding somewhat chauvinistic, it's also at least partly a guy thing, somehow we just can't resist measuring and comparing :-)!
Back in the day, I used to hand load magnum handguns. That was when having a Weatherby really meant something, and unless you could afford a Weatherby, you couldn't afford a chrony. But for what they go for now, I feel they are an important part of a shooters tool kit, especially when used properly. Properly would go something like this, in my opinion:
New gun, routine out of box maintenance, as you described.
Break it in, 500-2000 pellets, depending on gun. Don't worry much about accuracy or best pellet yet, just shoot it.
After break in, determine typical range and target, then find 2 or 3 most accurate pellets.
NOW do your chrony testing, both to establish a base line, and to determine which of your accurate pellets gives the best power FOR YOUR PURPOSE, bearing in mind that best power may not be most power. The flip side being, most power may not be most accurate, but it might still be accurate enough. That was the case with my old .177 CFX, most accurate was JSB Exact 4.52, but Superdomes were almost as good, and delivered about 2 fpe more. Superdomes were and still are the best all around pellet in that gun.
Like I said, this is my opinion of how it SHOULD be done, but that doesn't mean that's how I'm doing it :-). Forgive my long windedness (quiet, Dan!), I'm sure most of this is obvious, but maybe it'll give the newbs a starting point that helps avoid some frustration or even buyers remorse. The most important point you made is to just shoot. NOTHING takes the place of practice, which builds confidence in your own abilities, and familiarity with the guns capabilities. I finally got out of springers because I never developed any confidence in my HW 77, which killed my self conficence. Went from 5 springers to 1 PCP, and I don't think I'll be going back. Too much work and not enough power :-)! And no, I don't know how much is enough, but I'm working on it. Later.
Dave