How common is this and how quickly would the magical ancestry show in a Muggle family?
Taken off Harry Potter wikia in reference to J.K. Rowling and the Live Chat, Bloomsbury.com, July 30, 2007 (2.00-3.00pm BST):
Muggle-born witches and wizards are descended from Squibs who married Muggles: the magical ability unexpectedly resurfaces after many generations.
They are much more common than Squibs.
While there is no known percentage of how much of the wizarding population is comprised of Muggle-born wizards, they are known to be much more common than another group - Squibs, which are said to be very rare. In the footnotes for “The Tales of Beedle the Bard”, JKR explains what a Squib is, and states that Muggle-borns are much more common than Squibs.
“2 [A Squib is a person born to magical parents, but who has no magical powers. Such an occurrence is rare. Muggle-born witches and wizards are much more common. — JKR]”
- The Tales of Beedle the Bard
This is also implied when Ron says that Squibs are the opposite of Muggle-born wizards, but Squibs are quite unusual - implying that Muggle-borns are much less so by comparison.
“A Squib is someone who was born into a wizarding family but hasn’t got any magic powers. Kind of the opposite of Muggle-born wizards, but Squibs are quite unusual.”
- Harry Potter and the Chamber of Secrets, Chapter 9 (The Writing on the Wall)
Therefore, since Muggle-borns are not considered to be ‘quite unusual’ like Squibs, Muggle-borns are presumably not particularly rare, though half-bloods likely make up the majority of the wizarding population.
I found a list of known Muggle-borns from Hogwarts and the Creevey brothers were the only siblings. I think it is highly unlikely that having more than one wizard in a Muggle family is common. Think of Lily and Petunia, or Dean Thomas and his sisters. Hermione was even supposed to have a Muggle little sister, but J.K. Rowling cut her out. So I am concluding that although descendants of Squibs will eventually have magic, it rarely happens in the same generation.