Madrid to Valencia

If you arrive in the morning then it's perfectly feasible. You need to get from the Airport to Atocha station: after a long flight, a taxi is best, the flat fare is thirty euros.
From Atocha station you have two options : either you buy a ticket for the next available train as you arrive, for about sixty euros, or you take the risk of prepurchasing a cheaper ticket in advance, which is lost if your flight is delayed and makes you miss the train.
I would go for the first option unless you are travelling on a public holiday, trains rarely fill up and are quite frequent (every 1-2 hours). But if that stresses you out, you should leave yourself a safety margin in the train booking: don't book a train earlier than 3.5-4 hours after landing.

This is an extremely helpful response. Thanks. We will want the high speed train, which I’ve been told is only about 1.5 hours. Is the frequency and cost for that high speed option what you were describing? We would purchase upon arrival at the train station, as you suggested.

Yes, high speed trains leave 10-15 times a day taking about 1:40 and costing about 60 euros full-fare - I'm seeing a few departures for 70 but otherwise they're all under 60.

Thanks again, Balso........please send the link to the site you are using for the train schedule.

You can check fares and timetable on Renfe website: https://venta.renfe.com/vol/home.do?c=_thgt

You can also get to Atocha Station from the airport by taking the airport express bus. The fare is 5.50 euros, and it goes to Atocha with only one stop at Cibeles on the way. Takes about 25 minutes, and it runs about every 20 minutes from Terminal 1 (to the far right as you come out the door).

For train schedule, there's Renfe as stated above, but I was/am using Loco2. Reputable agency, no mark-up, easier to use than Renfe. Works for several European countries.