I've been waiting to play a Dragonborn character for a long time...
First encountering them as a monster class as I made my way through the world of Krynn, first as a soldier in the free-armies of the War of the Lance, and later as a Commander of the forces of our Lady Takhisis.
4th edition Dungeons & Dragons put them on the map as a playable character, and I will admit publicly that I enjoyed 4th edition, having them now evolved to 5th edition D&D. So what can one expect playing such a unique heritage?
What is a good filter to view them through? Let's start with the +2 boost to strength, and the +1 boost to charisma. This puts them in naturally into the fighter/barbarian possible paladin class and the sorcerer class.
Get half way decent 4D6 drop the lowest rolls for these attributes, or roll legendary and your Dragonborn is in a good place. For the sorcerer class I'm not only looking at the +1 charisma boost, but also the strength boost- there are a few sorcerer builds that has the class working as a second line "fighter" type class similar to the monk and cleric. Sorcerer is a natural fit- but of course playing Dungeons & Dragons one can roll or role with any of the classes. Draconic ancestry. The real deal of the class.
Gives you a dragon-lite breath weapon that advances with class and the resistance to match. This is a nice backup attack regardless of class, but compliments really well with the sorcerer class- using it at lower to mid levels before it caps out as a primary attack- freeing up spell slots for other low to mid level dedicated attack spells, which can be dedicated to more area effect or out of combat use spells.
On the lower end spectrum of spells it frees up dedicating magic to attack spell slots. Making your sorcerer build potentially more diverse- you can always take more damage stuff and go 100% in arcane cannon.