In theory you should choose among these three specification using appropriate tests (test for significance of fixed effects to compare FE vs OLS, LM Breusch-Pagan test to compare RE vs OLS and Hausman or Ahn-Low test to compare RE vs FE) and present only the chosen specification. However in practice many researchers provide results for FE and RE (or even FE, RE and OLS) simultaneously and after that analyze tests results in order to indicate which specification should be treated as baseline. In many cases the above estimators are corrected for autucorrelation, heteroscedasticity or spatial dependence of error terms.
As Piotr aptly points out, the choice of model depends on the data, and what question you are trying to answer. If you are presenting results, you need to justify the approach you used based on the data and based on context expertise. You can't say "I used FE because that is what is expected when presenting an academic research project".
No, you do not need to report both. However, you should report your reasoning for choosing a particular strategy. In some cases, you may be interested in understanding the random variation between units, and in other cases you may be more interested in making inferences at the population level.
I agree with Linden. In my research, I always justify why particular methods or models are used. In sum, research objectives and theories supersede methodology, but on the other hand methodology provides empirical proof.
Presenting / reporting only one model / method is sufficient provided that we provides enough evidence to support that model (example: F-test, BP-LM test and/or Hausman test)