Is the series oriented more towards the sci-fi side or 'romance novel' side?
It’s a little of both. There’s a romance aspect to the first series, “The Parasol Protectorate,” mainly in the first book, but the series is more adventure than romance. There’s a little romance in the second series, “The Finishing School,” but as it’s more YA than the other two series, the romance doesn’t really come up until the last book. The third series, ”The Custard Protocol,” has much more romance than the other two, but there’s still plenty of action.
Gail is a romance fan, but much more of a SF/F fan. She builds out the world of the Parasol-verse in a strong way. She also has a good sense of humor, which is one of the delights of reading her books.
If you want to try, start with Soulless, the first PP book. If you like it carry on. If not, that’s fine as well.
By the way, though chronologically it’s Finishing-Parasol-Custard, you can read them in publishing order too. You won’t be lost.