Ippodo is a nice site, though you may feel like you have to go through the Spanish Inquisition just to make a purchase. The set Fatal refers you to retails at 3800 yen, which is about $33 USD. With shipping, that gets bumped to 5200 yen, which is about $45 USD. That's pretty reasonable for a matcha set, but still almost double the range you want.
If anyone asks, you didn't hear this from me...but you can make a very nice matcha using a small bowl or ramekin and a small whisk. That should be under $10 easy...under $5 if you're a shopper. If you're looking to get into matcha, there's nothing wrong with doing that to try it. Personally, I'd rather do that while saving up to get a matcha set I really liked rather than something cheaper.
I did google matcha sets, and about $26 was the the lowest I could find for a set...but I really didn't like them. They had shallow, curved bowls. You want something that is more ramekin-shaped...a flat bottom with sides coming up at almost a 90º angle. At the very least, you want a deep, curved bowl. It makes for an easier and more thorough (and neater) whisking job. In the $40 range, things started to look much, much better.
You can probably find a chasen for about $10 with shipping on eBay, and Japanese Green Tea Online
has a nice, attractive bowl for under $20.