Too many variables at play to give any sort of definitive guidance, so what we can offer you are merely individual preferences. For example my experience is that break-in seldom accounts for more than a scant fraction of an airgun’s overall accuracy potential. As such, I don’t want to spend a bunch of time on break-in only to then find out there is a substantial defect in the barrel or elsewhere that I could have long since identified.
So I start by looking everything over for any loose fasteners or parts not fitting well, and check that moving parts operate correctly (e.g. bolt and trigger). If I identify any issues, I address them before moving on. Otherwise I clean the barrel and mount a scope and grab some cheap pellets to get it roughly sighted in. Then it’s straight to the better pellets to get a sense of what it likes and its capacity to group. Later, I may return to the cheaper pellets if it manages to group them well enough to be interesting, like punching aspirin-sized Mardi Gras beads at 30 yards or the dime-sized ones at 50 yards.
If you’re new to the hobby, you will be acquiring knowledge at your own pace and prioritized in a way that is most meaningful to you. My way of doing it may not be right for you. Bottom line, if whatever approach you choose…if it’s not fun, change it up. If there’s a technical hurdle, do a search or ask the forum. There aren’t many things you could encounter that would be new to us.