Gosh. Hard one.
Favourite PC is pro'lly the name I picked for this forum: Lt. Cmdr Michael Barratt, 1/4 Betazoid, 3/4 Human, CMO of the USS Perseus. His older sister had no empathic abilities, and his father, a 1/2 Betazoid and 1/2 Human neurologist, hadn't really thought it would pop up. When it did, Barratt left London and was raised for basic empathic training on Betazed with relatives. He didn't really study it much, didn't really like his abilities (he felt very isolated among full telepaths, and awkward), and his empathy was so weak except for one area: he was very good at sensing pain. It led to a similar career as his father: medicine.
In the past, during an away mission when he was a Lieutenant, he was part of a team trying to rescue a group of hostages. Pirates unleased a plasma weapon - a very painful experience - and even though he wasn't hit, the empathy overwhelmed him, he cried out, passed out, revealed their location and was captured - and people died in both the attack and the rescue of the Doc.
Andrus Hagen (from that ep with the nightmares and Troi and sleep deprivation) was called as an expert on Betazoid telepathic abilities during the formal hearing that happened thereafter, and recommended that Barratt be discharged from Starfleet. Instead, Starfleet Medical made him undertake a tour on Earth, with mandatory training in the handling and use of his telepathic abilities. Since then, he's honed his abilities and finds his empathy (especially his ability with sensing pain) is a handy diagnostic tool, but he still nearly always refuses to rely on the ability at all. He's got a major case of guilt over the dead rescuers, and he tends to get stiff about the rules and regs in SickBay. He's recently started to clue in that he needs to work on his mental abilities again, and has started bi-weekly "meditation" classes with many of the other crew.
The Doc (who'll have to think long and hard for Fave NPC)
So you think, 'Might as well,
Dance a Tango to Hell,
at least I'll have Tangoed at all.'
-- "Rent," Jonathan Larson