Batteries, charger and radios are easy.
http://www.hobbypartz.com/fs-g2-24ghz-radio.html Great basic radio, not lots of adjustments, but really inexpensive. Can't beat $20!
http://www.hobbypartz.com/73p-ac680-accharger.html Charges all kinds of batteries, including LiPo, when you get there. $50

Those will work with any car or battery you choose. Being that you guys are new, and the Frog comes with a brushed motor (if I'm not mistaken) you might want to start with a couple of NiMh (Nickel-Metal Hydride) batteries. Those are fine for brushed motors. And will last you fine until you get good enough at driving where you'll want more power/speed, and will want to go brushless. However, I HATE the battery connectors that Tamiya uses. The first thing you should do is ditch it, and replace it with Traxxas type connectors. Convert everything: charger plug, battery connector on ESC, and battery connectors on batteries you buy. These connectors are made to handle high-current, UNlike those crappy white Molex connectors Tamiya uses, which can melt.

When you are ready for a brushless system, this is a great one:
http://www.hobbypartz.com/ezrun-35a-9t-3650-motor.html Only $80 I run these on my Evaders.
For LiPo:
http://www.hobbypartz.com/98p-40c-50...se-direct.html $42!!

The only thing about HobbyPartz is, when they have something you want, better order it. If it goes out of stock, you'll wait six months for it to come back into stock. They have to send a new container ship from China, after all. You may have the wherewithal that you don't need to buy budget stuff or want to "Buy Amurican". In which case there are a few "sportsman class" US makers, like Castle Creations and Novak for motor systems, HiTec for servos, Futaba and Airtronics for radios. And of course, Traxxas. Most hobby stores that cater to RC carry Traxxas, almost to exclusivity, because Traxxas makes it so easy for stores. Check out your local hobby shop (LHS) to see what they carry, especially when it comes to parts. It sucks having to wait a week to drive your RC because you broke a part. Having the ability to pick one up at the LHS makes for happier kids.

Hang out on these forums and read read read. Ask questions. Research.
Ask yourself: "How good am I with my hands at repairing and working with small parts, and soldering?" (There's something else you'll need: Soldering station. Have you done soldering before?)

There is tons of stuff to learn, but don't let it overwhelm you. That's what we're here for. Lots of folks here willing to give you their two cents.

I hear a good number of people started out with a Tamiya Frog. Are you guys going to build a kit? Or a ready-to-run?