The [del]Northern[/del] [del]Western[/del] [del]Southern[/del] local Stickverse pantheon is feeling bored and the deva in charge of reincarnations is off sick. They decide to kill two birds with one stone by messing around with the next person in line to be born. That person is you, you lucky dog! You have a choice of three less-than-perfect Order dads: Eugene Greenhilt, Tarquin, and Ian Starshine. Pick the lesser of three evils (well, technically, the lesser of one Evil and two Goods).
You may or may not have left out the most important OotS dad of all: Varsuvius.
I think I’d go with Eugene. Tarquin suffers from that whole “Evil Magnificent Bastard” thing; not being evil myself, I’ll pass. Ian and Eugene are closer, but Eugene strikes me as being a bit less screwed up, both personally and in terms of parenting skills. Plus unlike Roy I’d like to be a wizard; we could have father and son “hey, let’s go and make fun of the fighters” bonding moments.
Eugene. My methodology is simple - look at current outcomes: Roy, Haley and Elan. Now, which of those three is *least *screwed up? IMO, Roy by a country mile.
One might argue that these are all despite parenting rather than because of, but still, that’s consistent for all 3. If I have to choose someone to ignore, Eugene seems easiest.
Your methodology is flawed. Elan is far and away the most balanced, mentally healthy person in the Order. He has good self-esteem, he’s friendly, relentlessly optimistic, generous, and strongly moral. He’s also dumb as a box of rocks, of course, but that’s not due to upbringing. Out of the entire Order of the Stick, Elan clearly has the upbringing to most be desired.
Elan, of course, was raised by his mom.
Now, if we look at Roy, Haley, and Nale, then Roy gets the gold medal in the “Not a Psycho Olympics.”* So I agree, Eugene is the winner here despite himself, but for slightly different reasons than yours.
Ian laid a trip on Haley so deep that trying to resolve it shorted out her speech centers. Ian clearly loves his daughter, but his parenting left her an emotional cripple. Eugene is a crappy dad, but mostly because he was distant and uninvolved. I don’t think growing up to be a wizard is going to help much in your relationship with him, though. I get the impression that Eugene was a crappy dad even before Roy was old enough to decide not to go to Wizard School.
[sub]*Haley takes a respectable silver. Nale kills the ref and burns down the stadium.[/sub]
I’m going to have to go with Tarquin, if only by default. Eugene is a dreadful father who actually murdered one child through carelessness and arrogance, has shown nothing but contempt to another, and overindulged a third. Ian seems like the nicest of the three, but he has definitely raised Haley with a skewed view of reality that almost shattered her mind. Tarquin may be very, very evil, but he’s a loving father who has his children as his top priority, unless they try to betray and kill him, which I would not plan to do.
Now, would I want to be married to him? I would not.
I think that Roy doesn’t mind that his dad is a wizard. What he minds is that Eugene thinks that fighters are worthless.
I want Tarquin to be my daddy. I think that I have a great underdeveloped talent for evil, and Tarquin could help me maximize my potential in that area. Tarquin genuinely loves Elan and wants him to be happy, but sometimes doesn’t understand why a Good bard would be upset at seeing his name in lights. Eugene doesn’t really give a crap about Roy, since Roy isn’t interested in being a wizard. I thoroughly enjoyed Roy’s time in the afterlife, where Roy got to bond with his granda. Ian loves Haley, and she does continue the family line of work, but he did screw with her mind, and he’s trying to continue to do so.
I’d love to see Belkar’s dad. And mom. Surely halfpint homicidal berserkers (I know he started out as a ranger, but he seems to have that berserking down pat too) don’t start out that way?
I think the odds are high that Belkar’s parents are dead, and that he had something to do with it. 
I went with Monster-san’s dad, because there’s at least a chance that he’d be decent, but if I had to choose between the three, I think I’d go with Tarquin. Yes, he’s evil, but at least with him you know where you stand.
Tarquin, clearly.
Look, I know the evil/semi-good thing is in play here between the three choices but the simple fact is that neither Ian Starshine nor Eugene Greenhilt are self-aware enough to make good parents. They are BOUND to screw their kids up because they simply don’t care about them.
Tarquin, on the other hand, is a remarkably well-balanced personality who is encouraging to his children. Embraced one that turned on him then instantly embraced another in spite of the first child’s betrayal. He even supports and encourages Elan even though Elan’s stated goal in Tarquin’s destruction. That is, by any standard, above and beyond the call of parental duty.
He regrets being absent from Elan’s life, he wants to make up for it, and he shows an understanding of his and Elan’s roles and encourages his son to grow and try new things. Even when he gives advice to Elan it’s not in the ‘I know what’s best!’ thing but seems to be good advice aimed at helping Elan avoid pitfalls and eventually succeed.
Dear Lord, we should ALL have that sort of parent.