What are the best base weapons to upgrade for Lightning, Fang, and Hope?

Subjective to your job as well. Such as a fully upgraded Gladius would be best for Light as a COM but a Lionheart would be better as a RAV and so on.

Fang = Taming pole Most balanced but has stagger lock which isnt a big deal as long as your 2 other chars don't have stagger lock weapons
Lighting = Blazefire saber (most balanced for com/rav) quick stagger sucks ass so don't even bother with lionheart
Vanille = belladonna wand best debuffing.. and yes you'll do that a lot end game

That's my setup ^ all upgraded to t3

Hope would be his highest magic wep which is... Hawkeye or you could get the more balanced malphas

If you read around no one even mentions using a Blazefire Saber for Light. It's either a Gladius for high strength as a COM or a Lionheart for the quick stagger as a RAV.
Why do you think quick stagger sucks?

Because it's only 10% before and you're losing a lot of stats.

The blazefire saber is lights most balanced weapon. I use her as com/rav

While gladius is her best com weapon I like to keep her balanced as I use her as healer in certain situations.

I have no problem with the weapons I use.. I mean I have 100% completed the game and I kill shaolong gui's in 2-3 minutes, So I see no problem.

which gun/s did you go with for sazh

Rigels but I only upgraded them to t2, As I don't play him.

ahh.
well i'm currently using him quite a fair amount for farming turtles so i figure i might as well upgrade something on him.
i'm thinking either pyrocons or the stagger wep with 1005 str/mag at max lvl.

The procyons are terrible imo, Rigels would be the best bet for sure as it is his most balanced weapon.. As with all the other stagger lock weapons.