Start with The Warden. Now, mind you, the NEXT book in the series is a much better book, but The Warden gives you the lead-in to Barsetshire, Trollope's world. It was Trollope's first big commercial success.
The main characters in The Barsetshire series are pretty well all clergymen and their wives, but, believe me, these are NOT religious books.
After The Warden comes Barchester Towers, then Dr. Thorne, then Framley Parsonage, then The Small House at Allington, and last, The Last Chronicles of Barset. The Small House at Allington will remain one of my most favoritest books forever.
The Last Chronicle of Barset leads into Can You Forgive Her, which is the first in the Palliser series, which books are regarded as Trollope's masterpiece (along with The Way We Live Now). Then follows: Phineas Finn, The Eustace Diamonds, Phineas Redux, The Prime Minister, and at last, The Duke's Children.
Aside from these two "series" he wrote dozens of other books. I don't adore them all, but several of them are absolutely wonderful: Orley Farm, The American Senator, The Vicar of Bullhampton, Ralph the Heir, and Rachel Ray. And, of course, The Way We Live Now and He Knew He was Right.
The style is, of course, rather dated. You must be willing to become a Victorian, and you will NEVER be sorry.
I am always pleased to recommend Trollope. I think of the fun you're going to have, when you meet Mrs. Proudie.
And Mr. Slope.
Dig deeper.