Printing Postcards, Need Help Finding the Right Printer

Hi All! I am looking for some help with choosing the right equipment for our business. We currently do all of our direct mailing in-house. We send around 2,000 letters per week but would like to start sending postcards as well. I am having a hard time finding the right printer to handle the heavier stock paper. We would be sending out approximately 2,000 6” x 8.5” postcards per week. I am looking for a printer that is efficient on time and production cost. Would anyone be able to point me in the right direction or help educate me on my options? Thanks in advance!