Here's the short version:
It doesn't matter which religion we're dealing with AFAIK.
Have high diplomacy.
Don't have low diplomacy.
Unlanded characters are much easier to recruit - try to convince the spouses of rulers, so they can convince the ruler's heir to join.
When you're just starting, focus on high-diplomacy courtiers. High diplomacy makes them better at recruiting, and being courtiers makes them easier to recruit.
When making someone sympatheti:
The family argument works well against almost anyone with children.
The personal argument works well against friend, lovers, relatives, and people who otherwise like you.
If you want to induct someone into the faith, choose based on their education or lifestyle, unless both are intrigue. You can also go for community if they have kids, friends or lovers.
If you still don't know, start looking at traits - Brave, Gregarious, Erudite, Ambitious and Just are the ones that matter.
No matter what nothing will work against religious heads.
Be gregarious. It helps a lot when trying to convince people to stick around.
And here's the long version...
For developing sympathy, it always helps if the target is Kind, Just, Trusting, Patient or Charitable. Odds also improve when your diplomacy is above 12, 14 and 16.
As for the arguments, each argument is improved if at least one of the following is true:
Family
Gregarious
Socializer
Kind
At least one friend or lover
At least one child, if opinion is at least 35 (not sure if that means the child must like the parent, or vice versa)
Trauma
Craven
Kind
Scarred
Has any disease, disability, or negative congenial trait.
Profit
Greedy
Ambitious
Cynical
Administrator
Diligent
Smart, Genious or Shrewd
Any stewardship education
Personal
The target must have at least 15 opinion of you for this bonus. In addition, one of the following must be true
Target is your friend or lover.
Target has at least 50 opinion of you.
You are the target's direct liege or top liege.
You and the target are close relatives.
You have at least 15 diplomacy.
Each of these make the AI less likely to become sympathetic:
Target is Zealous
Target is Cruel
Target is Arbitrary
Target is landed (harder for higher tiers)
Target is a priest.
You have less than 8 diplomacy
Religious heads will never develop sympathy this way.
Trusting characters are always more likely to join the religion. Your diplomacy also helps (odds improve every two levels from 12 to 22). You can never convert the head of any religion. As for the different options:
The warrior option is more effective if at least one of the following applies (they don't stack)
Brave
Any martial education
Any martial lifestyle (I think that means duelist or strategist traits?)
Target is someone's marshal
The community option is more effective if one of the following applies:
Target is Gregarious
Target has at least one friend or lover
Target has at least one child who likes them or who they like, again not sure which
Target has a diplomacy education
Target has a diplomacy lifestyle (not sure what this includes)
The theology option is more effective if one of the following applies:
Target is an Erudite
Target has a learning education
Target has a learning lifestyle - not sure what this includes either.
And the legendary ruler one is more effective if one of the following applies
Target is ambitious or just
Target has a stewardship education
Target has a stewardship-based lifestyle
Targets are less likely to convert for each of these:
Target is a priest
Target is paranoid
Target is zealous (this is a big one)
Your diplomacy is below 8
Target is landed (it gets a lot harder as their rank goes up. Except against nomads.)
Credits to u/pjoelj