There are far too many great players to pick between four...so I'll make three: one for the defense, and two others for the offense (including a special one). I'm sorry, but I honest to fate cannot choose just four players to represent this franchise.
Defensive Ramsmore (from left to right): Merlin Olsen (for his longevity, reliability, and production in anchoring two Fearsome Foursomes), Deacon Jones (he coined the word "sack" and probably had more than anyone alive), Jack Youngblood (wasn't as good as Deacon, but was still an end who put fear into the hearts of the offensive linemen who faced him - and he happens to be one of the toughest players to ever play the game), and Night-Train Lane (an amazing cornerback in his era, and one of the fiercest hitters to ever play the position).
Offensive Ramsmore (from left to right): Orlando Pace (one of the unsung heroes of the Greatest Show on Turf, Pace was a fantastic blind-side left tackle for Kurt Warner), Isaac Bruce (absolutely one of the most underrated receivers in the NFL and in my opinion, a first ballot Hall of Famer), Torry Holt (an incredible player in his own right, who was literally the best receiver in the NFL for a time), and Jackie Slater (played his entire nineteen-year career with the Rams and was an absolute rock for the offensive line in all of those years).
The Ramsmore of Running Backs (from left to right): Eric Dickerson (a dominant force for the Rams, and his trademark goggles made him the face of the eighties franchise long after he was gone), Marshall Faulk (one of the most shifty players in the open field, an excellent receiving running back, and the catalyst for the Greatest Show on Turf), Steven Jackson (who - despite facing eight/nine-man fronts with an atrocious offensive line and pathetic leadership - never quit on the team, matured into a fantastic leader and the face of the 2004-2012 Rams, and put up phenomenal stats), and Lawrence McCutcheon (he's been with the Rams for almost forty years as a player and in the front office, and he's the fourth leading rusher in franchise history behind two Hall of Famers and a potential HOFer, which is certainly something to hang your hat on).