Would I initialize an integer for the motor speed and use for example "rightmotorspeed = atoi (serialreadvalue)"?
That depends on that serialreadvalue is. If it is an array of chars, and is properly null terminated, yes. If not, no.
How would I then determine between the left and right motor? What function would be required for this?
Again, this depends on how you are getting the serial data. If the data is stored in a NULL terminated array of chars, then strlen() on that array will give the length. The upper index is then one less than the length. The character at that position will be 'L' or 'R'.
byte index = 0;
// some code to fill the array
int servoVal = atoi(inData);
char servoLtr = inData[index-1];
If you send "147R", then inData will contain "127R\0", index will be 4, servoVal will be 127, and servoLtr will be inData, or 'R'.