Transferring data from Wii to Wii U should be safe, since the Wii U's Wii mode is completely separate from the rest of the Wii U. However, the transfer is one way only, and all the Wii's data will be removed upon transfer. It is recommended you do not interrupt the transfer at any time, or you might end up losing your Wii's data completely.
Games you bought on Wii are not directly compatible to the Wii U, you can still play and possibly download them using Wii mode. Games that are available on both the Wii's Shop Channel and the Wii U's E-shop, can be bought on the Wii U with a price drop if you own the Wii version and have transferred that Wii's data onto your Wii U. Keep in mind, that unlike Steam, PSN/SEN, and XBLM, purchases made on Nintendo's consoles are bound to the console, which is what makes data-transfer so important, and is also the reason why the old console's data is wiped afterwards.
As for which Mii takes precedence: you decide.
When you try connecting to an existing NNID with your 3DS, your 3DS will ask you if you wish to keep your Streetpass Mii, or overwrite it with the Mii already associated to your NNID. Unfortunately, I don't know if it's true for the Wii U as well. I suspect it might be similar, though. In any case, I'd recommend creating a simple Mii as your personal Wii U Mii first, then overwriting it with the existing one.