We play every year with all the extended family to save money. Ours is not a "White Elephant" which are traditionally gifts that nobody wants. But instead we have a $30 cap (paid, not value) on a cool gift. We all just call it "THE GIFT EXCHANGE".
As far as order, you can either draw numbers from a hat (what we do) or you can assign numbers in order of arrival (not so cool, since you want a lower number, so this encourages people to be late). You could also go by age, or alphabetical. But we draw so that every year it is a new chance for people.
We play a tree 'hand' rule, which is third hand to touch it, keeps it. So that would be opened (1), stolen (2), stolen again (3). The original opener may be the person who steals second (therefore keeps) but no one may steal what was just taken from them. If your gift is stolen, you may steal a different gift, or open a new one. If you steal, that person may steal another or open, and so on and so on until the last gift is unwrapped and kept by somebody.
Also, my family complains alot, so if people are not happy after 'round one' then we all redraw numbers and do a second round of just stealing. :-D We are on our 4th or 5th year of this and everyone really enjoys it. We play the Saturday before Christmas (this weekend!)
We don't have a seperate one for the kids, as they usually take one another's gifts anyhow, so we just assure that all kids bring a kid gift, and it sorts itself out. This keeps them involved with the whole family and saves time. :-P
Have fun and Good luck!