I just got in to reading Michael Connelly last year and really have enjoyed what I have read so far. Haven't read any Thomas Perry.
One of my favorite authors is Greg Iles I have read just about all his books. The Penn Cage series is really good (a new one is due out this year)
David Baldacci is't bad either
Of course there is James Patterson's Alex Cross series, Michael Bennett series, and Womens Murder club series.
I would start from the beginning but I'm told you don't have to read them in order. I finished Killing Field recently and I enjoyed that one a lot. I got 30 pages left in Die Trying while it's good it wasn't as good as the first one. I'm a newbie to Lee Child so I don't have much to offer except those two.
I really liked Killing Floor. As a second, I'd have to say Worth Dying For and Gone Tomorrow really drew me in. I've read about eight of them and all are pretty solid. In Without Fail, he's trying to stop an assassination attempt on the vice president. A really cool discussion about past assassinations and two movies where an assassin attemted to pull the trigger- In the Line of Fire and The Day of the Jackal. If you're a thriller fan at all, those two are must see and it was cool to see how the characters compared and contrasted them in the book. Child always does a solid job.
I would definitely start at the beginning with the Jack Reacher series. They are fast and easy reads similar to James Patterson's style of writing. In addition I can recommend the Joe Pickett novels by CJ Box.