Air carrier Captain reported a gear disagree and gear door caution message after take-off. Flight crew referenced QRH and returned to the departure airport.

Narrative

Last night while flying Aircraft X from ZZZZ to ZZZ we got a GEAR DISAGREE and GEAR DOORS caution message and discreet lights after we put the gear up after takeoff. I was PM and my FO (First Officer) was PF. I requested a heading and altitude from ZZZZ departure and told them we had a problem we needed to work out. We accomplished the QRH and then got in touch with flight control and Maintenance via AIRINC and we all concluded we should return to ZZZZ because the fuel consumption with the gear down would be too excessive to safely continue the flight. We then accomplished the deferred items approach checklist and returned to land. On final; when we put the gear down; we did not get a green light on the right main confirming the gear was down so we executed a missed approach and requested priority handling. I assumed control of the aircraft to make the landing. We then accomplished the GEAR DISAGREE QRH for the gear lever down without 3 green indications which led us to do an alternate gear extension and resulted in us getting 3 green. We then continued on in and landed without any further issues.