What, exactly, happened to the good thief on the cross, and why? (Catholic perspective)

Jesus says to the thief on the cross "today you will be with me in paradise" (Luke 23:43). What does this mean? Did the thief go straight to heaven when he died? Did he get to skip purgatory? If so, why? It would seem that he did no or minimal good works, and it's most likely that he wasn't baptised. Ideas that bubble to mind include perfect contrition, baptism of desire/baptism of blood, and also the idea that God is not bound by his sacraments, so this guy was a special case who received extrasacramental grace direct from Jesus. I'm not sure how to put it all together though.