I have a 2009 Mazda 5. 30,000 miles in and I am ready for new tires.

I am down to either a set of Goodyear Eagle GTs or Michelin Pilot Sport
A/S.

Anyone have a preference? In theory, my priorities are quietness of ride, handling, tire wear in that order.

 

Good*Year's are a no-no as far as I am concerned.
The Michelin's are good and there is at least one other member here that ran them, but they are EXPENSIVE too.
As I have said many times now, the best set of 4 for my car (so far) has been, and is the Continental ExtremeContact DWS. We put them on my wife's Vibe and are happy with them on both vehicles... and she can be harder to please than I am when it comes to tires.
They are a little softer in the ride department, braking is VERY good, as is traction in all conditions I have had to deal with, they are still "reasonably priced, and the wear rating is 540!!!
The only downside, and its a small one IMO, is that they are a little slow to react to steering input. I have mine pumped up to 38F/34R instead of Mazda recommended 32/32 and the Conti's are much better now.

 

I replaced my crap Goodyear Eagles after only 714 miles from the showroom; and I replaced them with (the then much less expensive) a set of Michelin Pilot Sport A/S tires. The Michelins served me well for just a tad over 48,000 miles, however, now that I've replaced them I realize just how incredily noisy they were. The tires I replaced the Pilot Sports with are the Yokohama AVID ENVigor, and I cannot say enough good things about them. The Yokohamas handle as well as the Michelins, they cost something like $70 per tire less, and they are so-so quiet that I'm still surprised how quiet my car is now, even after 8,000 miles on the Yokos.

The only downside to the Yokohamas compared to the Michelins that I can come up with is that the Pilot Sport A/Ss seem to have a bit more traction when the snow is heavy and wet compared to the AVID ENVigors.

 

I put your priorities (ride > handling > tread wear) into tirerack.com and it came up with the following:

Tire Search Results

 

I went with Michelin Pilot Exalto A/S from Discount Tire, though I downsized to 16" tires (205/55R16). Great tires, I'm pleased with them.