Trouble with most climbing plants is that they are, by their nature, fast growers. If you want it to cover the car port within the next 3 years, then it will require a fair bit of cutting back at regular intervals once established.
Do not on any account go for wisteria or russian vine as they are both high maintenance monsters that want to take over the world. Or a clematis montana. Lovely but monstrous.
And you want it to grow up wires? Not an easy ask. Virginia Creeper for instance needs a nice rough wall to cling to, and the same goes for ivy family. Are there a couple of pillars that the plants could use to get up there?
How much earth is there and is it any good? If some good soil I would go for one of the David Austin roses that would not want to get too huge, but would give a beautiful display. Generous Gardener for instance. But it would require annual cutting back without a doubt.