A few things to know about Georgette Heyer books. She practically invented the "Regency Romance," and no one has done it so well since. However, she wrote pretty much only four heroines, and she wrote nearly every story twice.
It's just that they are so well researched and form their own internal logic so perfectly, fans of her books simply don't mind.
The first one I read was Cotillion. It still has my favorite young hero. Also, a Young Lady Dependent on Stingy Relatives. Cotillion.pdf
Early efforts include These Old Shades and Devil's Cub, which are best read in order. They both are the kind of story that seem to begin right in the middle of something, but before long, you're in the middle of it as well.
These Old Shades.pdf
Black Sheep and Lady of Quality are extremely similar. They are the "on the shelf but doesn't care" late 20s heroine meets gentleman others dislike or fear, who is actually awesome type. I favor Black Sheep slightly over the other.
Lady of Quality .pdf
Arabella is just one of the best written. She's one of the Very Young But Practical girls who's always having escapades. Arabella.pdf
The Grand Sophy has an Unconventional Miss who delights clever people and worries dull ones. You will love her. The Grand Sophy.pdf
The Unknown Ajax is the Perfect Catch, Dark and Stormy variety. The other Perfect Catch variety is awesome but bored with being wanted so much... The Unknown Ajax.pdf