As a count, your main advantage is that you don't care about tyranny. You can get gold by searching for rich courtiers, imprisoning them, and executing or expelling them. Repeat ad infinitum.
If you are under a duke and want to overthrow them, the arguably best focus is the intrigue focus. You can spy on your liege until you get an event to imprison them, then declare a faction revolt and have automatic 100% warscore. If you can't do that, you can spy on other vassals to force them to join your factions. Once the liege has elective succession, you can make a faction on his primary title.
If your direct liege is higher than duke, just conquer 51% of a de jure duchy (usually by fabricating claims) and create the title.
You don't need to be the same religion as your liege all the time. If your direct liege is not independent, you can refuse title revocations and keep spying on him at the same time, while also being able to call in allies.
I've not tried the counts of Vermandois or the prince-electors. But if you try that, I suggest that you give your temple holdings to characters of any other religion than catholic. You'll be guaranteed to get some taxes and levies out of the holding.