There's something to be said about writing a successful series. If the first book does well, readers will want to continue to read about other characters and plot lines introduced in the first book. But will there be one big story arc, or will each book be read as a stand-alone?
I've read books where I was totally confused, then realized I'd come into a series midway. And because I was so frustrated trying to follow it, I didn't go back and buy the other books. I've also read series stories where the hero and heroine are in each book, and for me, that wasn't satisfying, because in some of those there's no happy ending. (I'm talking romance here, not urban fantasy, in which this seems to be the norm.) I'd have to read the next book to see that. So when I set out to write a series romance, it's about a central theme with a different set of protagonists in each story. Personal taste, mind you.
However, the book's ability to be read as a stand-alone seems to be the big question when it comes to successful series romance. As an author, you want the story to flow from book to book. But the new reader who didn't read book one has to be able to understand book three. Somehow, you have to give enough of the background so that new readers will understand while old readers won't be bogged down in a rehash of the story.
You also have to be consistent. Even the most minute recurring character has to have the same color eyes throughout the series. It can get harrowing keeping track unless you have a good system.
My latest series with TEB is the Storm Lords. Each book is about one of four identical brothers from a far off land. So in each book, I had to describe what their land was like, the villains they face, and what exactly a Storm Lord is without bogging down the story. It was a pain, but it's also a fun challenge to get it right. The real excitement was with character growth in the series. All the brothers make appearances in every book, but the focus is of course on the romance between one particular brother and the woman he falls in love with. Yet each brother gets to grow as he encounters obstacles and overcomes them.
There are a ton of great series at TEB, and I'm always happy to share news about books I like. Here are a just a few of the many I'd recommend, and in no particular order:
Cattle Valley by Carol Lynne
Untamed Hearts by Jenna Byrnes and Jude Mason
Were Chronicles by Crissy Smith
Circle of Three by Brynn Paulin
And of course, a few of my own:
Life in the Vrail
Enjoy your Sunday!