If I do the power as well, what size fuse do you recommend?

Just about any fuse will do, your player shouldn't ever draw more than a couple amps. If you're running your amplifier off of the same wire, it will likely need to be more than that. I run my amp and empeg off of the same power wire that runs to the battery, and I think I have a 15 or 30 amp fuse on that line.

But the more important thing is to make sure that the fuse is in a special weatherproof housing and is as close as possible to the battery, i.e., mounted in the engine compartment. This is so that your car doesn't burn down if the wire insulation gets frayed somewhere and shorts to the frame.