Deciding where to begin with Trollope is a challenge. The good news is if you find you like him, you have a lot of good reading to look forward to.
I've read five of his books so far and my favorite to date is "Can You Forgive Her". This book is the first of the Palliser Novels. The next in the series is "Phineas Phinn" which is also very good. I recommend beginning with these.
Also another thought, I recently read "Old Goriot" by Balzac and loved it also. Haven't read anything else by him yet, but he was also very prolific like Trollope.