I've selected one each from chromatic, gem, and metallic for presentation. As stated previously, the metallics are still shaking out to be a smidgen more powerful just because of the extra breath weapon in their toolbox -- even if said breath weapons can only be used a total of once before requiring a short rest to recharge it. For example, the silver dragon presented below would only be able to use cold breath or paralyzing breath once before needing the short rest, not both.
Self-proclaimed kings and queens of the chromatic dragons, reds are ambitious, arrogant, and aggressive. They strike first and hardest to obliterate opposition.
Ability Score Increase. Your Strength score increases by 4. Your Constitution and Charisma scores both increase by 2.
Fearsome Mein. You are proficient in Intimidation.
Fire Breath. You can exhale a 15 foot cone of fire as your breath weapon. This attack deals 1d6 fire damage per level, to a maximum of 20d6 at 20th level. At young age, the range increases to 30 feet. At adult age, it increases to 60 feet. At ancient age, your fire breath has a 90 foot range.
Fire Resistant. You are resistant to fire damage.
Capricious creatures, crystal dragons are seen as flighty and untrustworthy. There’s some truth to this, but crystal dragons live in the moment more than any other dragon breed and prefer talking to fighting.
Ability Score Increase. Your Dexterity score increases by 4. Your Intelligence and Charisma scores both increase by 2.
Size. Your size is Small. Your natural bite attack only deals 1d8 damage instead of 1d10. This damage increases to 2d8 at young age and older.
Charming Wyrm. You may use the dancing lights and friends cantrips.
Crystal Breath. You can exhale a 15 foot cone of glowing crystal shards as your breath weapon. This attack deals 1d4 damage per level, to a maximum of 20d4 at 20th level. Half of this damage is slashing, and the other half is radiant. At young age, the range increases to 30 feet. At adult age, it increases to 60 feet. At ancient age, your crystal breath has a 90 foot range.
Radiant Resistant. You are resistant to radiant damage.
Where gold dragons inspire awe, silver dragons inspire hope. They are the most beloved by their subjects and the most easily riled to defending the weak or the Council’s wishes.
Ability Score Increase. Your Strength score increases by 4. Your Wisdom and Charisma scores both increase by 2.
Cold Breath. You can exhale a 15 foot cone of ice and cold as your breath weapon. This attack deals 1d8 cold damage per level, to a maximum of 15d8 at 15th level. At young age, the range increases to 30 feet. At adult age, it increases to 60 feet. At ancient age, your fire breath has a 90 foot range.
Paralyzing Breath. You can exhale a 15 foot cone of paralyzing gas as your breath weapon. Those caught in the area of effect must succeed on a Constitution saving throw with a DC equal to 8 + your proficiency bonus + your Constitution modifier or be paralyzed for 1 minute. At the end of each turn, the victim may make another saving throw to end this effect. At young age, the range increases to 30 feet. At adult age, it increases to 60 feet. At ancient age, your weakening gas has a 90 foot range.
Cold Resistant. You are resistant to cold damage.
There are some bits I'm not sold on though, such as the cap on the breath weapon dice for some breeds to keep relative parity with their monster versions; a black dragon's breath is just not as strong as a red's at the top end. Should I forego that limitation and just let it rank up all the way to 20 dice for every breed?
Possibly. I feel like there's a case for some slight power disparity, but I also don't want five dice to be the reason someone doesn't pick a particular race. It's a roleplaying game after all, the min-maxing is only part of it (or not a part at all for some groups). So yeah, undecided as of yet, and can be convinced in either direction.
Dragon whelps (handle it) are undeniably stronger than comparable PHB races and I think that's perfectly fine for the kind of game you'd be playing. A red dragon baby is still the size of a fridge and can probably out-muscle almost any half-orc. They do still operate under the 20 stat limit of beginning characters, though I do have some special rules that I'll present later on regarding the raising of this limit as the dragon gets older (ancient dragons cap out at 30).
Another contentious point might be their resistances at character creation. "What do you mean the red dragon isn't immune to fire right out of the gate? You effing casual!" or something to that effect went through my head as something people might say. Full immunity at all times isn't very fun for DMs to contend with or players to wrangle, so I've gated the immunity behind a feat that I'll go into for a later entry.
I'll leave this off for now because otherwise this would explode out into a gajillion pages of class and feat discussion, but here's the gist of my thought train.