In a team setting as well as solo you have different choices for different reasons.
If you are in an escort and by yourself I would target another escort. As the chances I have to kill him will be greater depending on how fast I can take him out. An escort has the least survivability of any ship. Excellent for spike kill if done correctly. If you are in a science ship and by yourself target another science ship or cruiser. They are generally better targets. Bigger, slower and you will find your science skills stick to them alot more effectively depending on your setup than trying to hit a buzzing bee. And generally your job as a science captain in a science ship is to set up the escort to cut through ships that otherwise wouldn't go down. If you are in a cruiser target the enemy cruiser first. Another target just as slow as you. Easy to maintain a broadside on them and/or debuff them regularly as they can only maneuver as well as you can.
In a team setting your choices are unlimited. You could target the healer first and start the fight strong. Bring max pain an test the teams defense right off the bat. You could focus the escorts and start the fight more defensively. Allow the enemy team to make the first offensive move. Wait for the spike buffs to pop up and remove them and the ship that activated them from the match. Or you could target the sci. Take out the middle healing man/ debuff and disabler.
You can even fake your first target and switch to any one of the other two classes on the field. Sometimes your target will depend on the enemy team setup. Sometimes it will depend on how you want to test the enemy team for weak points in either their offense or defense.
Let no other player discourage you from what you believe you can achieve in PvP. Though you may walk alone through looming shadows of doubt cast upon you by your enemies. Forge your heart with iron casting its shape out of only your pure will to push forward. You will not be denied eventually.
I generally shoot a poo cloud, after the ships run into it, I click fire at will, click Sci team and Extend shields, get a glass of water, come back to my desk and then go after who is left standing.
But I guess everyone else does it differently.
In a PUG, I'll target whoever's out in front at the start, especially if it's "full impulse Leroy" in an escort as a previous poster so eloquently described it. Then I'll just look to see who is taking fire from another team mate, or wounded, and call them out to try to focus down. Some people I'm starting to recognize as squishy, and may pick on them. Lockbox ships are generally to be avoided until their team has been whittled down.
One of my favorite things to do on the KDF side is decloak my Pegh'qu with its nose directly between a Fed cruiser's nacelles. Then proceed to cannon him up the rear until he dies. Most Fed PUGs in cruisers and slower sci ships have no hope of getting me off before they die, especially the DPS cruiser types.