Taking train after arriving from US to Madrid then going to Valencia

The 10:30am train for Valencia departs from Madrid’s northern train station, Madrid Chamartin-Clara Campoamor.. That station is currently undergoing a massive €1 billion reconstruction project that will put the entire station underground when completed after three years.
When I was there in September the station was a disorganized mess. Just getting to the train departure platforms from the Metro/Cercanias train arrival point required walking a detour around the construction. It was a situation where you could see where the train platforms were— you just couldn’t figure out how to get to them. A station employee explained how to do it and basically confirmed it was a workaround taking about 10 additional minutes of walking with luggage in a station where the escalators were not functioning due to the construction.
If you want to buy a non-refundable ticket, a safer bet is the Ouigo Espana train departing at 11:15am with tickets starting at $33 from The Trainline. Tickets may be less on the Ouigo Espana website. You can wait until arriving in Spain to buy your train ticket, but as you’ve noted tickets for the 11:30am Renfe train are already running at $50-$70 and are likely to rise further by March 18. Having extra time should allow you to take the Cercanias trains to Madrid’s Chamartin station which depart from the one floor beneath Terminal 4 ( what I’d call the basement level).
Trains take 15 minutes for the journey and they run every 20 minutes. There are shuttle buses connecting Terminals 1,2 and 3 to Terminal 4.
If it looks like you don’t have time for all that, a taxi from the airport to the Chamartin train station takes 15 minutes.
Keep in mind that high-speed trains in Spain require putting your luggage through an x-ray machine at a security checkpoint and this requires a few minutes to do.
Have fun at the festival!

Thanks for all that great information! I am worried that it might take me time to go through customs and get to the train, etc. You mention that the Ouigo seems to be a good option leaving at 11:15am. Do you think that would give me enough time with the flight scheduled to arrive at 7:45am? Would it be even better to wait for the 12:30pm train? Is there much difference between the Ouigo and the Iryo and the Ave - or the Avlo? A few minutes faster or slower really doesn't matter to me. It looks like I could pay an additional 7 euros in order to be able to switch but that still would mean paying for the fare which it will be that day. Yes, since it's the holiday it seems like there will be a lot of traffic.

The 11:15am Ouigo train gives you 3.5 hours which should be ample time. The 12:30 pm train allows 4.75 hours which may be overly-cautious, but for $28 it’s a deal and you could eat lunch before boarding the train. The Renfe AVE train at 11:30am is $50, but with the departure just 15 minutes later than the Ouigo train, there’s not much advantage booking that train, in my opinion.
Any of these “should” be fine since the Chamartin train station is only a 12-15 minute taxi ride from Madrid Barajas Airport.

The Trainline says there are only a handful of tickets for these trains remaining, so you need to make a decision ASAP and book a train. With the finale of the festival falling on March 19, waiting until you arrive in Madrid to buy your train ticket could mean there are simply no seats on any high-speed train remaining for the journey on March 18. Trains do sell out in Spain for special events and holidays.

Thank you for all the information! I looked at all the possibilities and watched a video of the four trains and basically decided because the amount of time seemed best. I went with your suggestion to book the Ouigo at 11:15. I actually added on all the extras since that way if for any reason I need to cancel I can get 80% back. Plus I got to select a seat and have wifi, etc. All together it came to 46 euros.
I see that Iryo offers free travel on Cercanias to get to Chamartin. Does anyone know if Ouigo offers this as well?