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I've just been transported into a world where I have god-like powers, they are near absolute as far as I can tell, at least I've yet to find their limits.

The guiding principle of my powers seems to be "if I understand it, I can use it."

I want to experiment and figure out the extent of them, but also figure out the physics of this universe to extend my powers (assume physics comparable to our own).

As a fresh graduate of college in a science discipline, I have a broad but not very deep understanding of chemistry, mechanical physics, relativity, quantum mechanics, etc.

What would be a well informed testing regiment? What are some of first experiments I should perform to form a solid basis? Optionally later, what shall be my magnum opus? The test that justifies all this time and effort, and what does its results tell me?

META: I am new to this community, I don't know if this questions fits within worldbuilding, if not where would be a better place for it? Or simply a more fitting variant for this community?

Fortunately, you've given us a very important clue when it comes to figuring out the limitations of your new universe - it exist. This lets us apply logic from the fine-tuning problem.

All laws of nature stem from applications of the prior laws, for instance atomic interactions laws can simply be said to be a natural extension of the laws that create them in the first place, i.e. the Strong Nuclear Force and the Weak Nuclear Force. Right now, we've boiled the forces of the universe down to four fundamental forces (gravity, electromagnetism, strong nuclear force, weak nuclear force), and they're theoretically all unified in one force, the single unifying force (which is known as the 'Unified Field Theory').

Now, for a universe to have different laws from out universe, it needs to have a different Unified Field Theory - at which point the universe falls apart. Everything in our universe only works because of how finely tuned the forces are. If gravity was a magnitude stronger or weaker, we wouldn't have stable stars. If nuclear interactions worked differently, elemental atoms couldn't form or interact, depending on the forces. Any change to the Unified Field Theory means that the fundamental laws of the Universe now prohibit existence. That means since your universe exists, it now follows all the rules you know and love.

Is there another possibility? Yes. Since proving negatives is impossible, it's possible that another configuring of the Unified Field Theory could produce a workable universe. But that would be near-incomprehensible. Literally, we're designed to operate in a universe that obeys our laws, and a universe that obeys entirely different laws wouldn't be able to interact with you well. And, even in the event that you somehow could, you'd have to start from scratch. So, either you understand everything, or you understand nothing and are stuck doing everything from ground zero up.

This has a bit of a meta twist to it.

"If I understand it, I can use it" is pretty much the rallying cry of engineers. Once science is understood, it is applied by the engineers. As such, if you undertake many engineering tasks, you can build up confidence that you understand "If I can understand it, I can use it." Yay recursion!

Once that step is complete, you may wish to tackle understanding understanding. That's a monumentally challenging thing. Oddly enough, those who ascribe to "know thyself," have a strange tendency of arguing that anything they want to do is achievable. Food for thought.

First you need to verify the unaltered physics of your new home. Ideally, someone who does not have god-like powers should recreate Galileo's and Newton's experimental work (pendulums, centripetal force, etc.), while someone performs or researches the equivalent of Tycho Brahe's and Johannes Kepler's observational confirmation of orbital motion and a non-geocentric (or even non-heliocentric) universe.

While that work is going on, you could give someone a jump start on the knowledge to recreate Maxwell's electromagnetic equations, along with Franklin's, Faraday's, and eventually Stinmetz and Tesla's work with electricity and magnetism.

Starting from the knowledge base you describe, all of this should be accomplished (given a reasonable level of recruitment) in a matter of a few years.

The real trick will be biology -- unless you understand biology better than our society, you can't extend your own life to god-like immortality. Better get the smart folks on that one.

Harry Potter and the Methods of Rationality is mostly about this. For example in chapter 28 Harry uses his scientific understanding for partial Transfiguration, deemed hitherto impossible:

"Fascinating," said Dumbledore. "It's exactly as he claimed. He simply
Transfigured a part of the subject without Transfiguring the whole.
You say it's really just a conceptual limitation, Harry?"

"Yes," Harry said, "but a deep one, just knowing it had to be a
conceptual limitation wasn't enough. I had to suppress the part of my
mind that was making the error and think instead about the underlying
reality that scientists figured out."