If you want to make the game more realistic think of reasons in nature why the dragon might have feature X, Y or Z.

For example a bright purple dragon (just coming up with the first random thing in my head) wouldn't be any advantage, it wouldnt be able to stealthily hunt prey, or hide itself from threats.

Breathing fire however could be a very useful tactic for any carnivore, as not only can you kill your dinner with it, it's pre-cooked so you spend less energy digesting it.

Again, horns might have an evolutionary reason, as would plumes on the back of the neck etc.

If youre unsure about your idea, don't be, because i think youre generally on the right track. Just think how many species of birds there are in the real world and base your dragon designs of avian features for example, this will give you lots to go on. Are some dragons nocturnal? Do some hunt different prey than others? Is there such thing as a herbivorous dragon? Is there a flightless dragon? etc etc.

Good luck with your game!

This is more a aesthetic issue, do I want there to be dragons with so many different attributes that it looks like there's several species of dragons, or make it subtle, make the race look unified, and base it on real world differences within species, mainly size and shape of certain parts of the body.

How particular are you about this "species" thing? If you describe dragons as being of the same genus, you can get away with a bit more variation. You could even step up to the same family but different genus or sub-family, etc.

Consider a felidae panthera tigris (tiger) vs. a felidae acinonyx jubatus (cheetah). To most people, those are just two very closely related animals that differ primarily by stripes vs spots, yet they're each a separate genus (panthera vs acinonyx) and even in separate sub-families (pantherinae vs felinae).

And the common house cat (felidae felis catus) is in the same family felidae as a lion (felidae panthera leo). Which is a really big difference, despite both being "cats".

Jumping down to just the species level, though, of course you can get away with a lot. Coloration, habitat, size, behavioral patterns, diet, mating rituals, poison, etc. can all vary between species of the same genus.

How important is it for the game play that the player be able to easily tell dragons apart?

The more important it is to be able to tell them apart (or more difficulty that will be caused by NOT being able to tell them apart) the more important it is to make them visually distinct.

This is all about the look of the dragons, not their characteristics that affect the game's design, so I'm moving this to Visual Arts. (Personally I think the different looks ought to be accompanied by different behaviors, capabilities, and/or AI.)

Forgive me if I've missed this in the thread, but what sort of overall aesthetic are you going for? Is the world presented in a very realistic style? A painterly style? A cartoony style? How are you depicting humans?

If you have a slightly cartoony style, then a little bit of exaggeration might be acceptable--you're not depicting the dragons as actually being all that different, but are depicting them via caricatures. This might be reinforced by a subtler art-style in cutscenes, showing the dragons more accurately.

Otherwise, one thought that comes to mind is sexual dimorphism: certain characteristics might occur more frequently or be more pronounced on either male- or female- dragons. You might also find this Wikipedia page useful.

sounds like you need a distinct enough look for each dragon so the player can tell them apart.

and you need a solution that does not require a lot of art work.

so the thing to do is figure out how to make them distinctive with the least amount of artwork (or an acceptably small amount of artwork).

that would probably be using different colors for the various parts of a dragon. its pretty simple to change the color of a graphic in a paint program. you could throw in a few different graphics as well, like small vs large horns - stuff that's easy to make by just scaling existing graphics. you might even use a single set of graphics and procedurally change colors as needed, or procedurally generate multiple sets of graphics in different colors as needed from a single set of base graphics. IE let the code make the additional artwork for you.