War God is the most competitive. Strong footsies,pressure,mix-ups and relative to most of the cast good damage. Has some issues versus zoners as he has no fast long range options without meter.
Sun God: You get a command grab. It's ok footises still but far less overall options and pressure. You will mostly be about tic throws.
Blood God: You get 48% BnB combo, but have no way to land it. You have no tools or options and your better normals can't be used as they aren't safe in this variant like they can be with War. Great way to learn base fundementals of the game though. Mostly your goal is to sneak out crystal totems and then block forever until you can punish or EX parry punish something.
As for basics for war god.
B22~ Sword
F1B2~ Sword
114~ sword or air grab
Basic combo would be something like:
EX DB1, F2, B122~db1 (if starting with the sword for its armor)
or the EX DB1 may not juggle well if they are already juggled in which case use DF1 instead.