Version a) and b) are correct and they mean the same. Version b) might have a little more personal touch than a) which sounds a bit "businessy".
Version a) is the only possible construction if you decide a "direct object", as in
Ich entscheide etwas.
Also, if you decide something that concerns only others you cannot really use the "mich" version. That might be the case if you're the boss in a company or something
Ich habe entschieden, dass Matthias das Projekt übernimmt.
This is especially so, once you put the whole thing in third person
Er hat sich entschieden, nach Rom zu fahren... ist ok
Er hat sich entschieden, dass Thomas nach Rom fährt.... ist nicht ok
Version c) is always wrong but might be heard in Berlin dialect.