I understand that, but is it just a neat mathematical model to treat particles as excitations of fields because it makes calculations especially easy or is there really a field out there?
Combinations of excitations can be interpreted as different excitations, and by 'can be interpreted' I really mean "can spontaneously transmute into" according to the probabilities of quantum mechanics. Since all interactions occur in discrete units of these fields (except for the photon field), referring to these units as particles is a convenient and compelling approximation - but it doesn't tell the full story.
Basically, it very much seems that fields are the more fundamental concept.
Compare http://plato.stanford.edu/entries/scientific-realism/ (and references therein)