Do you recommend taking a bus, renting a car, or taking a train for this route, trying to get there as soon as possible. Also, I know ferries run from Algericas to Tangier. Anyone know if Gibraltar also runs ferries, and which ferry is the fast one (where that one leaves). I heard there's a 45-minute one and a 2.5 hour one

We bussed it. Very quick. There is even a public bus that goes diretly from the airport to the bus station. Also, a pretty ride.

Ferries, there is a fast ferry. From Tarifa it would have been 35 min, so from Algeciras, an hour seems likely. But advice from this board convinced me to stay put in Tarifa/Puerto. I am glad I did, not because of what Tangiers had to offer, but for what I would have missed in Tarifa/Puerto.