[Rduke55]

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In dog breeding it's usually father-daughter...

Don't know if this would be best for humans or not.

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That's very interesting, thankyou. I looked up dog breeding on Wikipedia but it didn't tell me anything.

I did however find this tidbit of info on the Wiki:

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The Rothschilds

Among the descendants of Mayer Amschel Rothschild, the founder of the famous financial and banking family, many of the men married their brothers's daughters or cousins related through the male line.

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I don't know what the genetic effects of an "uncle-niece" offspring are, but perhaps this is the most preferable way for the children in my example to breed? (benkahuna where art thou?)

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Still bad, but uncle-neice share 25% of genes on average compared to 50% for father-daughter. So, if it's a choice, marry your neice before your daughter if you're going to have kids.
But considering that many states prevent first cousin marriages and they only share 12.5% of genes on average, then it's probably best to avoid any of this, Rothschild's plan aside.

Look at it this way. For a recessive gene disease (where you need 2 disease genes to get he disease) two people carrying one disease gene each have a 25% chance of having a child with two disease genes (and therefore the disease).

So take cystic fibrosis (CF). It is thought that something like one in every 25 or 30 of certain Europeans are carriers (meaning they have one non-CF gene and one CF gene). So just mating with a random person in that population you will have 1/25*1/25 chance they both will have a disease gene (1 in 625). Then they have a 1 in 4 chance that both of them will pass their disease gene on to their child. So a random pairing in this population will have a 1 in 2500 chance of having a child with CF.
However if it's brother and sister if one carries the CF gene then there's a 50% chance the other one does too (unless both parents are carriers - but that's not neccessary to talk about for this idea). So instead of 1/625 it's 1 in 50 that they both carry it which results in 1 in 200 chance of having a CF child instead of 1 in 2500.
For uncle-neice if the uncle's a carrier, the niece has a 25% chance of being a carrier, so 1/100 they both carry it resulting in a 1 in 400 chance to have a CF child. For 1st cousins it's 1 in 800.
This isnt the exact calculations but it should give you the idea.
Someone check my logic here. It's been a long time since I took genetics.