Help on count dependent variable


I am new to this forum. I am bombarded by a lot of info on count DVs. Here are my variables:

a. DV= firm-year observations. 7 years, 101 firms. I recorded the number of actions of a firm per year. The resulting measure is a Herfindhal-type of index since I measured the proportion of each action to all the possible actions. (This still remains a count or becomes continuous?)

b. IVs
1. Propensity to network= count variable
2. Strength of ties= number of hours per week spent * number of years of doing business (continuous var)
3. Network prestige= count variable

c. mediating var
1. action aggressiveness= ordinal scale (likert scale)

d. moderating variable
1. competitive environment= likert scale type

I am honestly confused on how I categorized the variables. If I made a mistake, please do correct me!

I hope that you guys can help me on which method to use. I am faced with using Poisson regression or GMM or GLS .