Yes, you can.
There are several mario games available on the Wii Shop channel's Virtual Console. Such as Super Mario Bros 1, 2, and 3. Super Mario World, Super Mario 64, Super Mario RPG, and more. All located on the wii shop channel.
The wii shop channel is used to buy downloadable games. You must have an internet connection to use the channel. There are two types of downloadable games. One of them is the Virtual Console. The Virtual Console is where you can download Old-Skool games made for previous systems. Not only nintendo systems either, besides the NES (Nintendo Entertainment System), Super NES, and Nintendo 64 there is also the NeoGeo (Ever seen arcade fighting games around? Odds are; it's a NeoGeo game.). There is also Sega Consoles; Such as the Sega Master System and the Sega Genesis. Then there is the Turbographx16, made by hudson (the company who makes alot of mario spin-offs, such as Mario Sluggers, Mario Party, etc.).
Gamecube games however; are NOT available for download; as they are already playable by just inserting the game in the disc drive. Just like wii games. But, you need a Gamecube controller(s) and memory card.
Sega Master System= 500 Points
Super NES=800 Points
There are exceptions; though. If a game was never released in the region your wii is registered to, there is an extra 100 point charge.
If there are licensing fees (such as Teenage Mutant Ninja Turtles; NES) the title will be extra because of the money it cost nintendo to get it on the virtual console.
100 points= 1$
You can find wii points cards in most places where video games are sold; or you could use your credit card to purchase them at-home. The only amount you can buy is 2000 points. 5000 points cards are only available in Japan for Japanese Wii's.
Amounts you can buy with a credit card:
1000 Points (10.00 + Tax)
2000 Points (20.00 + Tax)
3000 Points (30.00 + Tax)
5000 Points (50.00 + Tax)
And the games you got; Super Paper Mario is good. The rest aren't...Spyro is mediocre. Thrillville is fair; but there are much better games than it.
If you need help on which games to get for your daughter, you could email me at firstname.lastname@example.org. I know of everything good that comes out for wii and it's shop channel.