I hope you now can see that is was not so easy to translate your symbols.
Art first, you should learn to distinguish between static (ohmic) resistors which are characterized by capital letters (R) and differential resistances (which are also very important), which are written as small letters (r).
Thus, your gain formula as shown above is
gain:G=(Rc||Rl)/Re
However, please note that this formula is not correct because
*the minus sign is missing (inverting operation)
*The transconductance g of the BJT is neglected.
The correct gain expression is
G=-gReff/(1+gRe)=-Reff/(1/g + Re) with Reff=Rc||RL
As you can see, the transconductance g may be neglected only for Re>>1/g . The validity of such a simplification must be checked from case to case.
As you probably knows, the value of g must be chosen and depends on Ic (g=Ic/Vt).
Thus, your design starts with selection of Rc, Re and Ic (assumption: supply voltage fixed) .