Should gifts be small enough to fit through a mail slot, or will you be handling distribution for us?
Not necessarily. Anything you can package the US Postal Service (or a competitor) will ship, in my experience. When we did this on hfstival.com back in the day, people got cardboard models of Ronald Reagen, a guitar, and other large items.
I will not be handling distribution. Please factor shipping costs into your budget when shopping.
And what of perishable gifts? Or gifts of service?
I'm not going to make any hard and fast rules on this unless there's some overwhelming consensus demanding it. As a general suggestion as someone who has done these before, use your best discretion.
If it's illegal to mail _____, maybe it's not the best idea to purchase ______ unless you plan to hand deliver it. Donations to charities are much more appreciated if you know that charity is near and dear to the "gift recipient" not yourself. If it's a "gift of service" (I'm assuming you mean, for example, a masseuse giving someone a certificate for a free massage as a gift?) I'd make sure the person lives close enough that taking you up on it isn't an inconvenience for them and you have a good-faith belief they will actually enjoy the service. Unless you are really good friends with someone outside of the board and know they will share your sense of humor, joke gifts are probably a bad idea (e.g. sending a known Nationals fan Orioles merchandise or vice versa).
We are all adults who have ostensibly given gifts many times before, just think it through before you commit.