What are the important differences between fixed and random effects and which one should I choose?
The first point is that you should analyse your review in both ways (i.e. select first one option then the other in RevMan) and see how the results vary. If fixed effect and random effect meta-analyses give identical results then it is unlikely that there is important statistical heterogeneity, and it doesn't matter which one you present. If however, your results vary a little, you will need to decide which is the better method on which to base your conclusions (usually it will be best to select the most conservative option).
There is a great deal of debate between statisticians about whether it is better to use a fixed or random effect meta-analysis. The debate is not about whether the underlying assumption of a fixed effect is likely (clearly it isn't) but more about which is the better trade off, stable robust techniques with an unlikely underlying assumption (fixed effect) or less stable, sometimes unpredictable techniques based on a somewhat more likely assumption (random effects).
Sometimes the point estimate of the treatment effect differs between fixed and random effects because of publication or quality related bias. This may indicate that careful investigations are required, perhaps with expert methodological input. If this is the case in your review you should check with your review group.
Keeping it all in context
It's important to remember that whatever statistical model you choose, you have to be confident that clinical and methodological diversity is not so great that we should not be combining studies at all. This is a judgement, based on evidence, about how we think the treatment effect might vary in different circumstances. This judgement is a common source of disagreement about the results of meta-analyses. Make sure you spend enough time considering this judgement in some depth before you worry too much about which statistical model you choose.