All very good advice. I might add:

The less expensive tanks tend to limit the amount of abuse they can handle, i.e., outdoor, cross country stuff. For 1/16th scale, Tamiya would top the list for reliability (as TomZ recommends). Otherwise, you might wind up spending most of your time repairing/replacing parts, which can become pretty frustrating. A lot of guys upgrade the less expensive tanks (like Heng Long) with heavier gear, like motors, speed controllers, drive sprockets, idlers, track, and so on. In the end, you might wind up spending as much for upgrading a Heng Long as you might for a new Tamiya.

You might also want to look at the 1/6th scale M5 Stuart Light Tank (eBay always has some). However, it's a relatively cheap version of the larger scale tanks (usually around $150 ea shipped). And like its smaller 1/16th scale brothers, it's restricted in the abuse it can take outdoors. There are upgrades available but again, costs can climb quickly.

If you want to consider the higher end, more highly reliable 1/6th scale tanks, the price jumps dramatically to around $5500 per (example: armortek and others).

There is also RC Armory's 1/8th scale that comes in at around $2400 shipped. It's highly reliable and just a bit smaller than 1/6th scale and twice the size of the 1/16th scale tanks. (I have their King Tiger and it's loads of fun -- it weighs around 70 lbs).

Also, retailers might also offer a break if you purchase three of any kind. (BTW, if you're going to play too, wouldn't you need four?) Maybe get two and designate two kids per tank (I'm including you as the bigger kid) -- one can be the tank commander and the other the driver or something like that...

Cheers and good luck.