A couple questions. What's your smoking source? Grill, smoker, Alton Brown special?
Does your family prefer fatty or lean? For pork, I prefer the fatty... actually for beef, too since they are both long cooking applications.
For pork:
Fatty:
I like the Boston Shoulder (also called Boston Butt which is strange since it comes from the front shoulder), not many people keep them whole if they get butchered, most guys make it into sausage. I also like ribs, and I prefer the untrimmed spare ribs, but some people get a little squeamish about the cartilage and bits. Any are fine though, St. Louis cut, or baby backs have less mess. Farther on down is the picnic shoulder, and then maybe a sirloin roast. The hams are great cured and smoked, but I've never attempted a whole ham.
Lean:
These are harder because the fat doesn't render since there isn't much in a lean cut. If you have a pork loin (not the tenderloin) with a decent fat cap on it, you can smoke this and trim it after smoking.
For beef:
I like a full brisket, with the deckle left on. A lot of times this also gets removed in butchering. A trimmed brisket is tricky business because it's so lean. Also, beef ribs are fun, and are monsterish and kids like em.
Doneness: It's a word, dammit. I like my BBQ falling off the bone tender (even ribs, which some people say needs to have some 'bite'). Do you all have a preference?