Here's what Nintendo said in a recent interview:
SourceCan games be stored on external media such as SD cards, and what happens if you run out of storage space?
Nintendo: Games that are downloaded can be stored either to the Wii's internal memory (512MB) or onto SD cards, which plug into the SD slot on the front of the Wii. In addition the console also stores a history of all of your downloads so that if you have to delete any VC games for any reason you could re-download them for free at a later date.
Will you be able to take your VC games to a mate's house, say, on an SD card?
Nintendo: No. All VC games will be locked to the console they are downloaded on so even if they are on an SD card they can't be used on other machines. You will have to take your Wii with you.
Does that mean that if your console breaks you lose your VC games forever?
Nintendo: No. Nintendo will offer support to help Wii owners with problems to recover their games.
I'm not sure about Virtual Console game size, but I'm pretty sure the NES through all the other consoles, stopping at the N64 games, which will take up a good amount more, will be modest in size. I'm sort of hoping Nintendo allows for online storage of games. This wouldn't be great for those without an internet connection, but for those that do, it would open up a lot of space.
Maybe, in the future, Nintendo will increase the size of Wii's internal storage to a gig or two. Who knows?