Is a wild-type strain more "fit" than its mutant strains?
I will assume the mutation is not under some kind of balancing selection such as negative frequency dependent selection. As fitness is conditional upon the environment, I will assume a constant environment (heterogeneous environment can also lead to balancing selection).


  Is WT expected to be the ONLY strain to persist in the long run?


Yes. In fact, even if the mutation was beneficial, as it starts out at low frequency it still has a low probability to actually fix (fixation = reaching a frequency of one).


  How common is this scenario?


Mutations happen constantly. For example, every new human baby carry something like 10-100 new mutations that were not present in any parent. Most mutations are neutral or deleterious, only very few are beneficial. New mutations have a low probability to reach fixation even if the mutation is beneficial. The exact probability depends upon the selection coefficient $s$, the dominance coefficient $h$ and the effective population size $N_e$.


  What about co-existence?


In absence of balancing selection (or frequent recurrent mutations) and assuming that ressources are limited, then one strain will necessarily end up fixing. Note that this is also true under genetic drift only and does not even require any selection.


  Examples and references for beginners will be very appreciated.


Evo101 is a very short, very easy introduction to evolutionary biology. You should probably have a look at it.

Then, for something a bit more advanced, and because your background in mathematical modelling, I recommend having a look at the book Population Genetics: A Concise Guide by Gillespie 

For more book recommendations, please have a look at the posts


Books on population or evolutionary genetics?
Text Book Recommendation: Organic Evolution