It's an interesting sub-plot, but not essential to the game (although there could be consequences for your romancee later on in the game).
IIRC, romance is possible only if your character is human, elf or half-elf.
If your character is male, you have 3 possible choices of romancee. If female you get only one (and by all accounts, not a very good one at that).
There's no quest per se that triggers off a romance, all you need is to have the NPC in your party. Sooner or later it'll start. And watch out for the fireworks, and catfights!!
And welcome to the board, BTW!
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"Butt-kicking for goodness!" - Minsc
"Cities always teem with evil and decay. Let's give it a good shake and SEE WHAT FALLS OUT!!" - Minsc