I am no fragrance connoiseur, but I am learning perfumery, and I am very involved in the indie perfume scene. Let me know your aesthetic, or an aesthetic you're interested in, as well your favourite smells and your price range, and I'll give you a perfume recommendation to try out.
In this scenario, "indie" is short for "independent". So, an indie perfume house is run by the head perfumer and the perfume is made in-house rather than being outsourced to a factory.
The perfumes tend to be less "mainstream-smelling"--as in, they don't have that sharp, loud smell associated with department-store fragrance. It's also much more common to see perfumery being done with an oil as a carrier rather than ethanol, so it's great if you have sensitive skin.
Indie perfume is often also less expensive than department-store perfume.
A quick guide on fragrance:
Perfume/parfum, cologne, and eau de toilette are not gendered words--rather, they signify the concentration of actual fragrance. Perfume is the most concentrated (20-40%), and cologne is the least concentrated (5-10%). I use "perfume" as a catchall for fragrance of all kinds. By the way, "perfume" and "parfum" are the same thing. Same concentration.
I wrote a very long post on another wiki about perfumery and the major misconceptions surrounding it. Here's the link if you're interested. https://lost-cities-keeper.fandom.com/f/p/4400000000000595249