When I first started playing campaign mode, I picked Al Gore because he seemed to have some fairly good stats: good intelligence and nothing very low except for charisma (also, I think his caricature is hilarious). But I found myself having a really hard time getting past the middle republican candidates, and decided I'd try the campaign again as a custom republican. I tried to figure out what the most importatant traits are, so I could make the best possible candidate and running mate.
IMO, the most important stats, in order of importance, are:
Stamina - This one's obvious, more stamina = more everything. Especially political capital, which requires only an expenditure of stamina.
Charisma - Charisma affects the effectiveness of your speeches and ads, which is most of the game.
Experience - Candidates with more experience get endorsements for less political capital. Getting endorsements is the only part of the game where you're in direct competition with your opponent: getting an endorsement he wants gets you the benefits AND denies them to your opponent. So experience is very important.
Money - In the economy of the game, you've got to spend money to make money. More cash at the beginning directly translates into lots more cash throughout the campaign.
Fundraising - Another source of free money.
Compassion - I'm not totally sure about this one. From its description, it sounds like it has effects similar to charisma.
Most of the rest of the stats are 'core issues,' they just make certain voters like you more. These are nice to have, but no big deal. The last two traits, comeliness and intelligence, only affect TV appearances.
For my custom candidate, I maxed out all 6 important stats, which left a few points left over to spread between core issues, and made his homestate California so he can fund-raise there ASAP. For the VP, I just maxed out money and spread the rest among the core issues. The idea here is that the candidate is a campaigning machine, and the VP is just there for some more cash and likeability. I totally ignored the stats that help TV appearances, so I can ignore them in the game, too. I just cruised through the entire republican campaign with this pair. I think a custom candidate is much better than the candidates that you can choose from at the beginning, but some of the unlockable candidates are better. For instance, the top democrat has tens in all the important stats except money, and the rest of the stats are good too.
I think I've got this pretty well figure out. But I'm still unsure of some stuff. Anyone else got a good custom candidate? See any chinks in my armor? Is ignoring TV interviews a bad idea? What exactly does 'compassion' do? Which of the core issues is most important?