Don’t worry about standings with pirate factions. They’re basically irrelevant in Empire space. You can decline missions that require shooting empire factions - you won’t lose standing if you don’t shoot them! It helps to have a few agents you can do business with - declining more than 1 mission in a 4 hour period will cost you standing with the agent.
Easy way to repair standing as a new player is the SOE Epic Arc which will give you roughly 8% standing boost for the empire faction of your choice with no derived loss - depending on social skills. You can run the Arc every 90 days.
The career missions will give you roughly 7.5% standing boost - you can only run missions for a given agent once but each faction has 3 sets of agents.
Edit: the standings boost is a percentage of the difference between your current standing and +10. Important to realize this. The law of diminishing returns will apply as your standings improve.