It was the Rams, Colts, Bear, Niners, Packers, Lions all in the NFL West.
The first true 'rivalry' I felt with the Rams was the Colts. I can remember when the Colts departed feeling remorse that the rivalry had come to an end.. Ram's had not exacted enough revenge on them at that point and now they never would.
In 1958 the Ram's did pretty good finishing 8-4... so the first truly "Rams are winners" season for me came in 1966.... same teams as above but with the addition of the Vikings.
In 1967.... to this day probably the most exciting season I ever experienced.... 'today's league', IMHO, first began to form.. and the Rams were in the Coastal.. Rams, Colts, Niners, Falcons.
I'd have to say the 'oddest' alignment began in 1970.. Rams, Niners, Falcons, Saints. That seemed very goofy to me. And that group lasted a long time.. I forget the year it changed.
Occasionally I have wondered if the west coast should come together.. a division of Rams, Niners, Raiders, Chargers, Seahawks... but nah... need to represent both the NFC and AFC.