Teaching Fellow vs. Postdoc
In part to forcefully disagree with @Buffy's remark that it's generally easier to move from research to teaching roles... my own and others' PhD students from my "R1" university in math in the U.S. have encountered disbelief about their sincere interest in teaching at an undergrad institution... Indeed, given the way computerized job applications often work (mathjobs.org), it's nearly effortless to apply to any place listed on mathjobs.org. In particular, making such an application is absolutely not a proof of sincere interest, beyond not wanting to be unemployed.

I suspect significantly for that reason, some (I don't know what fraction...) of non-research-fixated math depts in the U.S. simply do not list themselves in mathjobs.org, so that "the bar" to apply to them is set higher than clicking boxes.

So far as I can tell, "sincerity" (or its appearance, ack, ...) plays a significant role. I see this, and am not entirely opposed to it, in graduate admissions, postdoc applications, and tenure-track applications. So, if one intends to "game" the system (well, why not?) one needs to do so well enough to fool a certain number of people.

Depending on your personality, it might be less stressful to just follow the direction you want, rather than having your day-to-day life determined by some dubious long-term strategy.