Cell phone in Spain

Either method will work fine. But if you buy a phone here, you must be SURE it's unlocked and quad band. If you're not sure how to do that, better to get it there, since a phone bought in Spain is guaranteed to work in Spain. If you go to a phone store to buy a SIM, they will sell phones too, and it won't take much longer to buy the combo than just a SIM card.

If you have AT&T or T-Mobile here in the US (or know someone who does), and have an older phone not currently being used, you can try to find out if it's quad band (for instance, the Motorola RAZR is quad band). Then you can call the carrier to see about getting it unlocked. If you can do this, you have a free phone that can be used in Europe. But again, if you're not sure it's both quad band and unlocked, leave it at home and just buy one in Spain.

Of course, if your child already has a T-Mobile or AT&T phone here, see if it's quad band and can be unlocked; then, they just take their regular phone with them.

One advantage of taking a phone with you over buying it there is that you can program in the numbers in advance. The other is that you know how it works, but most kids can figure that out in minutes [g].

One other advantage to buying a phone in Spain, it will have a charger with a plug on that fits Spanish sockets (and most other European countries). A 2nd hand phone from the USA will need a plug adaptor, and worst case a voltage converter.
Cheapo phones with SIM cards cost about €15-€19. Cheap!

Thank you Chris and Harold. I know I would have more peace of mind if we bought one here but a lot of good it would do if it does not work there.

Buy it there. There are plenty of options. You get a pay as you go SIM card, phone and charger, plus minutes for as low as 25 euros (for a basic phone). You can pick it up at a Kiosk in the airport or at the many mobile phone stores in town.

The only advice I'd add is to let the sales person set the phone up and make sure it works before leaving the store. You have to drop by a store to add value to the SIM. Other than that slight inconvenience, it couldn't be easier.

We packed Ipods for email, skype, internet and only used the phone to call ahead and book rooms as we traveled. WiFi is as ubiquitous as phone stores (if nothing else every McDonald's and Starbucks has free WiFi) just ask.

You can buy a cheap phone in Spain for about $20 and works fine. Just buy a sim card with a plan and you are good to go. I actually have my cheap phone with me and now don't need it as I now have an unlocked phone that works anywhere in the world. I purchased a Movistar Tuenti sim card for $27.00 USD which gives me 1GB of data and 100 minutes of calling and text. Will be fine for a month. My cheap phone doesn't need data, just calling and messages so it would be cheaper. Just go into any cell store, and there are LOTS of them so don't worry!

When is your "child" coming?

My daughter is currently in Spain for a semester , and has been using a T Mobile postpaid phone. Works virtually everywhere, free texting, free data, and twenty cents/minute for phone calls (works better in Europe than USA!). Doesn't solve the issue of a Spanish phone number, but would allow her to have communication until she gets a Spanish phone.
If you know anyone with an existing account, they could add a second line for $30/month, with no contract, or third line for $10/month. You can buy Windows phones for less than $100, and TMobile will unlock them. (It used to require service for a month or two to get unlocked, may have changed recently.)
Feel free to pm for additional info, and hope she enjoys it. My daughter is really enjoying it!