I'm sticking with the randomized idea. Rufus seems to have brilliant ideas so if he was thinking the same idea it seems pretty good. As for some players getting better items than others? Well, they could all add items that are similar to each other. But honestly you should be thankful for whatever you get. I used snowball launcher, ice dagger, etc as examples because the items should all be something really neat. It won't matter which item you get because they would all be really nice gifts.
If there was any other idea I had to choose from i'd definitely go with street's idea. Being able to choose your gift doesn't seems so bad either.