Air carrier pilots reported after takeoff receiving an ENG OIL PRESS R warning and returning to the departure airport.

Narrative

On day 0 at approximately XA:40 PM local time; we experienced a ENG OIL PRESS R indication shortly after takeoff out of ZZZ which resulted in checklist required inflight shutdown.Prior to the flight; nothing was noted as abnormal during the aircraft walk-around or preflight. The pushback; taxi out and takeoff were routine and normal.At around 800 ft. AGL; we got a ENG OIL PRESS R caution message and the oil pressure indicator was in the red band. The captain immediately instructed me to get the checklist out and ready and instructed the First Officer (flying pilot) to continue flying as normal. We continued to climb out and clean up the aircraft as normal and I informed the Captain that I had the (757) ENG OIL PRESS - L(R) checklist ready. Once they were done with the after takeoff checklist and we were stable; he called for the (757) ENG OIL PRESS - L(R) checklist and I believe it was at that time that he requested priority handling and asked to level off at 6;000 ft. They designated the flying and the communications with ATC to the First Officer while he and I ran the (757) ENG OIL PRESS - L(R) checklist.We ran through the checklist which led us to the ENGINE FAILURE OR SHUTDOWN checklist. The checklist instructed us to shut down the right engine and then we paused the checklist briefly at the point where it instructed us to choose between a restart needed or a restart is not needed. We discussed briefly on whether or not we each thought a restart was necessary. As a group we decided that since the oil pressure was in the red band; we would not restart the engine. The captain also reached out to dispatch and Maintenance Control to alert them of our situation as well as get their input on whether or not a restart was warranted.We continued being vectored by ZZZ departure control and the Captain called back to the Flight Attendants to alert them of our situation and to let them know we would be landing in about 20 mins with no need to brace. We also discussed the landing performance of the aircraft being overweight at flaps 20 with an engine failure. As per the checklist; we calculated the Non-normal landing distance using the Engine Shutdown row for a gross weight of 230;000 lbs and 20° above ISA. We calculated about 4;500 feet required. The First Officer then did an approach and landing brief and we continued the ENGINE FAILURE OR SHUTDOWN checklist. We then advised air traffic control that we were ready to start the ILS approach to XXL. The approach and landing were uneventful and the landing was smooth. Since our approach speed was higher than normal; firm braking was necessary to slow the aircraft. I don't recall which taxiway we turned off of XXL but I think it was either 1 or 2. We were then given instructions to cross XXR and contact ground.Once we got onto taxiway 3; the Captain pointed out the brake temperatures on the right main landing gear were showing values of 8. I pulled out the hot brakes checklist; ran through it and determined that we had brake temperatures in the warning zone. The checklist advised not to taxi for 60 minutes so we stopped and released the parking brake. The Captain used the aircraft tiller to keep the aircraft from rolling the First Officer advised ground control that we would need the crash/fire/rescue trucks to approach the aircraft and inspect the brakes.I made an announcement to the passengers that we would be stopping to have the emergency vehicles approach the aircraft to inspect the tires. The crash/fire/rescue trucks approached and advised us that black smoke was coming from our right main gear and they advised us that they were going to spray it with water. Once the brakes were cool enough; the crash/fire /rescue personnel approached the main landing gear and measured the brake temperatures. They advised us of the temperature and in accordance with maintenance we were given the go-ahead to allow the aircraft to be connected and pulled to the gate by an aircraft moveteam.They towed us to the gate with no further incident.