First, let's talk about threat. There are a number of ways that an opposing ship can present a threat to your gang, but these generally fall into two broad categories; Direct Threat and Indirect Threat.
Direct Threat is a measure of how much damage a particular target can do to you and your gang. Broadly speaking, high dps ships generally present a strong direct threat while low dps ships do not. However, some ships might be more or less dangerous in different situations. For example if you're flying in a fast kiting gang, you would probably consider a long ranged damage dealer like a rail Naga to be more dangerous to you than a short ranged brawler like a Brutix, even though the Brutix has a higher damage output on paper. Similarly if you're flying in a frigate gang, you'll be more worried about ships which can effectively hit your small frigates (such as destroyers) than those which can't.
Indirect Threat (sometimes also called 'tactical threat') refers to ships which aren't necessarily a danger in themselves, but which inhibit your gang's ability to operate effectively. ECM is an excellent example of an indirect threat - while it presents no danger in of itself, jammed ships are unable to participate meaningfully in the fight. Other common indirect threats include logistics ships (preventing your gang from destroying your intended targets) and tacklers (reducing your ability to escape or manoeuvre effectively). Again, consider what has the most impact on your own gang - a Rapier is a huge threat to kiting gangs but not worth worrying about if you're brawling. Similarly logistics ships are only a significant threat if you don't have enough damage to break through their reps, after which they become far less important.
There's no strict method for evaluating how much threat a particular ship presents, but it's worth keeping these two concepts in mind when you're considering what an opposing gang is capable of. Apply your own judgement as an FC to determine which threats are most significant to you.
A simple solution to target calling is just to go for the highest threat first, and then work your way down from there. While this would work, it's not the most effective way to go about it. Think of it like a race - if you can destroy their threatening ships faster than they can destroy yours, you win the fight. In order to do that, you need to consider how quickly you can take a particular threat off the field.
As an example, imagine an opposing gang consisting entirely of Drakes and Caracals. The Drakes do more damage, making them the bigger threat. However, Caracals are far more fragile - you could easily kill two Caracals in the time it takes to kill one Drake. In other words, you can reduce the opposing gang's damage output (their direct threat) much more quickly by targeting the Caracals first than you could by targeting the Drakes.
How quickly you can kill something isn't quite as simple as how much tank it has. Close targets make good primaries because you can begin applying damage immediately rather than wasting time getting into range. Similarly a target which is already tackled (particularly if they're scrammed and webbed) is usually a more reliable kill than one which can still escape - forcing a target to warp out is only as good as the time it takes for them to come back. Often in our roaming gangs we'll jump into a gate camp, and the first ship that someone calls tackle on become the first primary regardless of what it is, simply because it allows us to start firing immediately on a target which is already caught (obviously this relies to an extent on our gang members tackling sensible targets). Similarly in a highly mobile fight with ships kiting each other around, our primary choice will often be completely dictated by what is closest and what is tackled.
Remember that there are more methods of removing a ship from the fight than simply killing it. Electronic warfare can be a great method of taking a key ship out of the equation, whether that's damping down a logistics ships so it can't provide reps or setting ECM drones on a hostile recon to break their tackle. This allows you to suppress some threats while you focus your damage output on others.
The big advantage of EWAR is that (aside from ECM), the effect is instant and guaranteed. It also works at range, so offers a great way of dealing with targets that you're unable to catch. The main disadvantage is that you're limited by the number of EWAR modules that you have available - if you only have four damps (and assuming you need two to effectively take someone out of the fight), that means you can only suppress two ships at a given time. You also rely on that EWAR modules remaining present - if your EWAR ship gets jammed, damped, or destroyed, then whatever they were suppressing is immediately back in the fight.
Don't Worry, Be Happy
Calling the right targets is something that people worry about a lot, often without reason. This is an exact science, and there's really no such thing as an absolute 'right' or 'wrong' decision - it's really just a case of going with your gut and making an educated guess.
Your main priority as a target caller is to make sure everyone in your fleet knows who they should be shooting (and ideally, to make sure they're all shooting the same person). It's better to make the decision quickly and confidently - even if your choice isn't the best - than to spend too long trying to figure out the perfect strategy and leave part of your fleet confused about what they need to be doing. If in doubt, just pick the closest ship to you and then go from there.
Don't forget that you can change primary even if they aren't dead yet. Many new FCs will pick a target and stick to it, even when better targets present themselves or it becomes obvious that the current primary isn't going down any time soon. While you don't want to be switching primary all over the place without a good reason, try to pay attention to how the overall fight is progressing and don't be afraid to switch if a better opportunity appears or if your current one is going nowhere. That's particularly true when you're fighting a gang with logistics ships - a target which is already being repaired will be much harder to kill than one which isn't, and a fast target swap can often catch hostile logistics pilots unaware.
Let's finish off with a few examples. I'll make a post later this week explaining my own answers to each of these, but in the meantime I'd be interested to hear your own thoughts; In each situation, which ships would you go for first, which would you leave until later? Are there some ships you'd choose to suppress via EWAR or chase off while you kill the rest of their gang?
You: 10 mixed t1 cruisers with frig support
Opponent: 3 drakes, 3 caracals, 1 raven, 1 blackbird
You: 20 t2 frigates (mixed assault ships and inties)
Opponent: 3 zealots, 1 curse, 2 purifiers, 1 abaddon, 1 heretic
You: 3 mid-range battleships (e.g. pulse abaddons or AC tempests), 1 arazu (point and damps)
Opponent: 4 hurricanes, 1 broadsword, 2 jaguars, 1 stiletto, 2 scimitars
You: 5 kiting battlecruisers
Opponent: 2 megathrons, 2 vexors, 2 brutix, 2 enyos
You can read my answers here