What Is the Difference between RLS, LMS and Wiener Filter? When Is One Preferred Over Another?
All three are Estimators / Predictors.
All of them try to estimate the coefficients of Linear Filter which minimizes an MMSE Cost Function.

The Wiener filter assumes all data is given and sets the way to calculate the optimal solution.  

The LMS and RLS are sequential / on line methods to solve the same problem and given the data is stationary they all will converge to the same solution.  

The LMS / RLS can adjust their solution according to data and hence are suitable in cases the model changes in time.

The easiest to implement with the least computing resources needed is the LMS and it is the one you should start with. The LMS works on the current state and the data which comes in.
The RLS, which is more computational intensive, works on all data gathered till now (Weighs it optimally) and basically a sequential way to solve the Wiener Filter.

So, I'd start with the LMS.
If the model is constant and the LMS Convergence rate is good enough for my problem I'd stick with it.
If it seems I need faster convergence rate then I'd go with the RLS.