A couple additions:
Friendly Civilians are very important. As mentioned, if they are friendly then you can easily get resources (Goons, Rez, Data) from them. Goons and Rez are essentially free, while Data can be purchased with Goons - that you got for free from a Colony system.
For me, early in the game beams are a bit easier to use. Though they have a shorter range and consume a lot of power, it's easier to get hits since that beam is steerable during its ~3-second firing period. They can also make it easier to avoid accidental hits against friendly faction ships, which could hurt your relationship with that faction.
Later on, after acquiring more tech and larger ships, I'll mix up beams and cannon on one vessel. In that way, a single ship will be able to deal good damage to both the shields and hull.
Don't forget that you can adjust your fleet on-the-fly. Mid-mission, simply go to your design page, adjust the current design or choose another of your pre-configured designs, and then refit the ship. While you're continuing the fight, that ship returns home, gets refit with the new design, and then returns to battle automatically. This is handy with stealth missions since you can scrap 2 ships, refit the third into a speedy cloaking specialist, and complete those missions with near impunity so long as you're careful around the enemy.
Never underestimate the importance of Goons. They are currency for buying Data and for bribes, a larger crew makes your ships operate more effectively, and they provide a defense against boarding raids - this last is especially important once you start dealing with Zombies.
System Strength for Civs and UTA directly relates to the enemy ships you encounter and the size of their base in the system. If I find that, for instance, the Civs in a system offer for sale 2-4 bits of technology, but have low strength and aren't particularly friendly to me, I'll simply blow up the base; you get the technology once the base goes boom. Even though you've just pissed them off, they're now quite weak and won't be much bother to you.
System relations don't carry over from one system to the next, so don't worry about your actions in System A causing problems in System B. The Civs in A can hate you and the neighbors in B might love you. Until later in the game, Civ and UTA relations stay only within each particular system.
For quick restock of resources, always try to have a good relationship with at least some full-strength (3) Civ systems. Low on Rez after getting your clock cleaned in another system? Pop on over to the nearest friendly Strength 3 Mining system, refit your ships for max cargo capacity, and hang around their base to pick up Rez. If you're friendly with both the Civs and UTA in the system, so much the better so the UTA doesn't come pestering you at the Civ base.
Goon 'mining' isn't quite as simple, since you need to find a, um, I think it's Hotel mission in order to get the easiest Goons. Similar tactic, though now you're temporarily refitting to ships with a large Crew capacity. With the right ships, you can pick up a few hundred Goons quite easily. And the risk is very low unless UTA strength is high or you're in a high bounty situation.
The Bounty Hunters have some of my favorite ships so it's not necessarily a bad idea to keep them at least a little bit pissed-off at you. They are more powerful than the Civs and UTA so you will definitely have a tougher challenge. The flipside is that they also offer rewards for the arena battles. When my Bounty is high, I like to make certain that my Rez and Data are fully stocked before moving into Bounty Hunter systems - they can block your retreat from the system and take out the Clockwork in the ensuing battle if you're low on Goons and Rez and can't rebuild your lost vessels.
Speaking of arena battles, you can see beforehand what the reward will be. In the event that a successful battle will net you a Specialist, be certain that you have an open Specialist slot before starting the battle. These battles can be quite tough but there isn't any consequence for losing.
When fighting in a tough system, move away from your beacon. If your beacon gets destroyed you will not be able to get reinforcements, or refit / repair your ships during battle.