You actually can buy them online, or even in a physical store. You can buy Wii points cards. These can be bought online (Amazon.com, Target.com) or in the stores.

It's the same as buying them on the Wii, 100 points will cost you $1 USD, and they are only available in amounts of 2000 points, (so $20).

Glad to hear you finally got a Wii!!