Thesis research model question (long text)

#1
Hi everyone,
I want to ask a question about my master thesis for my next semester. I am a European economics student, my thesis will be within the field of Corporate Governance. I was thinking maybe you stats pros can help me, as I need help with the potential methodology/model and not the subject itself. To cut things very short, I will use a database on European firms to test how various corporate governance factors (things like board structure, size, and ownership variables) is related to innovation output (how much they spend on innovation for example) on the firm level, in different countries.

I am currently reading books on econometrics and Stata as per my supervisor's instructions, she said I need to use panel data. This topic (having innovation as the dependent variable) is not so well explored in my region that's why I wanted to do it. However, I need to know if the following makes sense to do from a stats point of view; Imagine that there is a ranking of countries on a kind of innovation performance, like 1-10 (best to worst). My idea was thus to add this factor to the model to incorporate this notion of country-level innovation, in our firm-level focus. I guess it would be used as a control variable, or is it an error term? Perhaps we could also introduce further country-level variables? Will this now become a multi-level model? I have read I could run into sample size issues if I do a multilevel model, due to the limitation of the number of countries.

If I use the ranking, how would I operationalize that variable, like dummy variable for e.g. 0 for low ranking and 1 for high ranking? Or can you leave this "open" somehow. I have had some feedback saying that a country fixed effect model may be suitable, I wonder if someone can expand on how this can help me, how would that model look?

Anyway, as you can see I am just starting off, but really would like some intuition from you guys, so I can come better prepared for my next supervisor meeting.