How can I pre-book a taxi in Schiphol Airport?

You can walk out of the airport and take a taxi from the rank, expect €40 to €60 depending on how busy the roads are.

Pre-booked taxis advertise from €20 for a car, but more often I see a price of €15 to €20 per person. So it is worth checking out the different websites if you go this route. (No links, as I have not used any of the companies, and can not pick one over the others.)
Most or all companies offering the pre-booked (often shared) taxis have websites on which they offer the service. Mostly you enter your arrival airport, date, flight, and expected arrival time and the company will check the flight details and make sure your flight is met, (you may need to contact them if you are delayed more than average in the airport, like when you have to spend extra time in immigration or collecting your luggage) and they will tell you where they will meet you.
You best run a search with pre-booked taxi or just taxi and the airport + city and those companies that offer the pre-booked ones will pop-up. Read reviews to get those that are safe.
I only used one once, when my planned arrival was shortly before the last train to my (smaller) station and the flight was also delayed. Good experience but several times the money I pay for train tickets, so only for late arrivals (which are rare for me.)

To compare, train tickets will cost you €4.50 (each) if you book online, €5.50 if you get tickets out of the ticket vending machines and €6 if you go to a ticket window.
Travel times will be comparable during the day, shorter by train in peak hours but, while trains run through the night, the go down to one per hour by one AM or so.
There are also buses if you do not fancy train travel.

I do not drive and as such I have little experience with collecting rental cars. I have noticed that it takes a bit of time, the times my boyfriend picked up a car for travel together, I am not sure whether that is the norm. When you google Amsterdam Centraal Station you will find several car rental companies pop up, most a little away from the most likely locations for your hotel.
I had a look at a car rental site and while they mentioned the option to use a rental car to go to the city, they did not mention drop off costs. It may be 'free' or cheaper than returning to the airport location, or it can be more expensive. Whatever you do, make sure you have up to date satnav/GPS as one way streets and busy bus and tram traffic in the area makes for need for more than two eyes.
Remember that Amsterdam is a city (if not a big one) and around the station traffic can be crazy.