I am just starting to get my feet wet with MBA research. A few questions I haven't been able to answer yet:

How important is a specific degree - or interest? I look at MBA as a way to expose myself deeper on topics I haven't really experienced yet? Is that too broad of a view?

Where is a good place to start for GRE prep?

MBA is a way to expose yourself deep (er) on topics that you haven't experienced. This is 100% true - However you need to think about what prompted you to feel the need for such an exposure?

Is it a specific job that you are targeting, or do you feel that you have hit a ceiling in your current role? Or is it anything else?

Usually GMAT is accepted in more program than GRE when it comes to MBA. For Masters in general (technical / non technical / management) GRE is widely accepted.

An MBA is management-oriented, and in that sense is rather broad.

A broad / general MBA is probably preferable for most incoming students, unless their goals absolutely require some kind of specialized knowledge (especially where there's strong overlap with technical aspects, such as data science or supply chain management jobs.)

But keep in mind that all MBA programs will offer at least some customization, whether through electives, projects, study trips, or other facets of the program.

Take the GMAT. Even if you are applying to non-MBA graduate master's programs (such as a Master in Management or Master in Finance), you'll go a lot farther with the GMAT compared to the GRE.