transport options

Casey,
"only 740 Km", that might not be far in Australia, but here it counts as a long way. For driving routes, and importantly times and costs, go to: https://www.viamichelin.com/ It gives: 724 km 07h38 96.31 € by the fastest route. Note time assumes no stops.

Driving from Amsterdam to Basel will be very boring, Autobahn all the way, and busy in places. Do you just want to get from A to B (literally), or enjoy something on the way? If you just want to get there, fly, that will be fastest. Train will be very comfortable, and faster than driving.
A cruise will be the slowest and most expensive option. It will provide oppurtunities to visit may places on the way (they include guided excursions), and see many scenic parts of the Rhine. Consider a cruise as part of your holiday. Do you fancy a slow sighseeing cruise, or is that not you? That should decide if you take a boat.

To get back to the car. Where are you actually wanting to travel from and to? A car is useless in both Amsterdam and Basel, and you can't park in either city centre, you have to park outside and get public transport in. And, one way international car hire has a large surcharge.
So what is your overall plan? where else will you be visiting? how does car/train or other method of transport fit into the complete trip plan?

Large stretches of the Rhine aren't particularly scenic and some parts are heavily industrialized. And although roads follow both banks of the river through the most scenic stretch, other portions of the river have no cooresponding road. So, although you could certainly pick a route from Amsterdam to Basel that roughly parallels the river, you would only see the river directly every now and again.

plenty of parking Parking usually isn't particularly difficult to find, with the exception of Amsterdam and Basel.

he best time to travel without to any tourists. Anytime except the summer.