Via USPS, it'll go by the size of your box, plus weight, plus destination. Anything over a certain measurement which qualifies it as "large box" incurs an additional fee. They make you sign a Customs form, which makes you list return and send to address, plus a description of the item(s) inside, plus its value. I think most people write "gift" just to be non-descriptive, especially for a Secret Santa. The value doesn't have to be accurate either, but I feel like that's an insurance thing and that's all they'll cover if the package is lost; correct me if I'm wrong. $10 is probably what you want to write there, regardless of the truth. The Customs form goes on top of the box, so your TT could easily see "Item: Fleshlight Comic Books" which would spoil the surprise. You can (and should) get tracking # for an additional fee, but I think it ramps the cost up quite a bit. As usual, be sure to tape the box up well and packing materials (bubble wrap, packing peanuts, whatever) since this international package will be handled much more than a national one.
edit: forgot to mention, they have these international Flat Rate boxes, where you buy the box and if whatever you have fits inside, it goes for the flat cost regardless of weight or destination. I don't know the prices, though.