I would use acid to lower your pH first, then add baking soda to raise your alk without raising the pH back up. If you do it the other way around, you'll raise the alk but then lower it again when you add the acid.

And yes, it's Arm & Hammer baking soda--the exact same ingredient as alkalinity up, at 1/5 the price.

I'd stop worrying about the phosphates--once you properly chlorinate your pool, it doesn't sound like algae is going to be a problem for you.

Janet