Killing time on the internet

I just found a neat problem on this page at Stan Wagon's site:

Suppose you are playing poker with a small group of companions and a single deck of cards. If Lady Luck guarantees you a full house, and you can choose which full house you will get, which one should you choose? Hint: The answer is not "three aces and two kings".

Hmmm—

The ranking of poker hands is

Royal Flush
Straight Flush
Four of a Kind
Full House
Flush
Straight
Three of a kind
Two pairs
Pair
High card

Since every full house makes two types of four of a kind impossible, I guess the the trick is that you want to choose a full house that will deny as many straight flushes and royal flushes as possible? With thirteen denominations

A-2-3-4-5-6-7-8-9-10-J-Q-K-A,

with A's possible at the "bottom" as well as the "top" on straights, maybe the 5's and 10's full house is better than A's and K's, since it makes more conceivable types of straight flush impossible ?

Uh—"more impossible," that is, if I choose my 5's and 10's so as to exhaust all the four suits.

I'm just making this up here, but I guess I've convinced myself that the A's and K's choice is not the best one, at least.

Maybe I've solved it by picking 5's and 10's?

Um, no, I'm not sure—I've also got to consider the number of possible full houses that beat me, since I'm not picking the best possible full house if I pick 5's and 10's. Yecch—now I've got to actually get out a pencil and paper.

Solution, please?

Added later: If I were a patient man, I'd consult this.