I have been using ATF or whatever PS fluid is on the shelf......I think Prestone in the yellow bottle.
That used to be my approach as well and it worked fine until I had a Jeep with oversize tires which stressed the power steering. Suddenly my choice of PSF mattered.
Now with my Buick, it matters because the power steering seems to be its achilles heel. It was very unhappy using old AC Delco PSF. It improved a lot after a flush and refill with new AC Delco PSF, but was still somewhat whiny and moany. New Lucas PSF offered more improvement, but still not perfect. Now the Lucas is 14 years old and it's getting worse.
This time I research PSF and various brands more carefully. For my Buick: Idemitsu, Amsoil, and Red Line all look excellent in their specs in data sheets. I expect good results from any of those. Idemitsu costs the least of those 3 and actually has the best specs.
Then there's my neighbor's Honda. It needs Honda PSF specifically. Well Honda PSF is made by Idemitsu. They're the same PSF. A 12 oz bottle of Idemitsu PSF costs $4.39 at Rock Auto, which is $1 less than same size bottle of Honda PSF from Honda dealership.
My other neighbor's Hyundai is not finicky about PSF. It works fine with any brand of Asian approved PSF.
Some cars aren't finicky about PSF. Some are. My Buick seems to be finicky in that it needs fresh top tier PSF to be happy. All Hondas are reputed to be finicky in that they're reputed to need Honda or Idemitsu PSF.
Jeeps aren't finicky with stock size tires, but with oversize tires they need top tier PSF. Ideally of a thick enough viscosity, which means any of the following: Idemitsu (it aint just for Hondas), Amsoil, Red Line, or Lucas. Lucas PSF is actually good stuff if you live in a moderate or hot climate where temps are don't get too frigid. However, the other 3 I mentioned are good in any climate.
What I just said above applies to Asian and American cars (which like thicker PSF, especially highend thick stuff). At least it applies if you have a finicky car or just care about your car a lot. If your car is not finicky and/or you don't care, then use whatever.
European cars are a different animal because they like good quality thinner viscosity PSF, such as Pentosin or Lubeguard Complete.
Valvoline synthetic PSF took a middle approach with a high quality medium viscosity PSF that probably works adequately for anything, though not ideal for anything. It's the jack of all trades PSF that's reasonably good for almost anything, but not ideal for anything.
I used Valvoline in a Jeep that had stock size tires and it was fine in that application.
It's also worth noting that (unlike motor oils) there are a lot of brands of low quality PSF. The worst often don't have a data sheet to look at. Some do and they will make you cringe if you read it. Oreilly Master Pro (house brand made by Prestone) is one such example, especially if you have a Honda, but really for anything else too. I assume Prestone PSF is that same cring worthy stuff. Read the data sheet and compare to other brands data sheets. You'll see signifigant differences.