CRJ-900 Captain reported that while hand-flying during the climb the Mach trim and stabilizer trim were inoperative; leading the flight crew to make a precautionary landing.

Narrative

Because the autopilot was deferred when we accepted the aircraft in ZZZ; the Captain; pilot flying; would hand-fly the duration of the flight. After departing from ZZZ; around 13;000 ft.; the Captain; pilot flying; noticed it was difficult to trim. Shortly thereafter we received the STAB TRIM and MACH TRIM caution messages simultaneously. Once the messages appeared; we ran the QRC and QRH checklists. After completing the checklists; the messages initially cleared but came back once the Captain attempted to trim again. We then [requested priority handling] with ATC and proceeded direct to ZZZ1 and asked that the trucks be ready for our arrival as a precaution. After completing the checklists; [requesting priority handling]; and making our arrival plan with the malfunction; we discovered the FO (First Officer) side trim was operational. We then decided I would continue the flight as pilot flying and perform the flaps 20 landing as directed by the QRH. Even though I was able to trim; we continued to treat the system as if it might fail at any moment; which is why we made sure to continue to follow the QRH checklist with the flaps 20 landing. It would be much easier and safer to go around in that trim position than at flaps 45. The flaps 20 landing was conducted safely with no issues.