The placement of now, on to the science depends on how you or the character you are writing about would say the words aloud.
Many years ago, I worked as a lab teaching assistant in a large university. If I gave a safety-related instruction such as "we need to put on our goggles for the next step", I would pause and wait until everyone was ready. In this case you want now, on to the science at the start of the second paragraph.
On the other hand, if I was simply describing the lab work in a tutorial where (obviously) goggles weren't needed, I might summarize the steps casually and finish with "and if we're all good with that, let's take a look at the science..." Then I would pause before I began talking about the main topic of the tutorial.
And one final thought: If you are writing a lab manual and want to sound casual in tone, read it aloud and see where the pauses fall naturally. That's where you should break the paragraphs.