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Those were going to be my two suggestion. If you've forgotten too much or never got that far in the first place, then they're not a bad start.

As long as you remember the basics of Newtonian physics, you could also just start on Griffiths quantum mechanics. Having linear algebra and PDE under your belt will help, but they're not strictly necessary, especially at first.

Stewart is my favorite textbook and my favorite calculus resource overall. If you prefer videos then Professor Leonard is also really good.

I did Newtonian mechanics and electrodynamics back then

At what level?

I’m currently selecting my classes and I have the option to take calculus based physics concurrently with Calculus II

Do this one. If they let you do it then it should be fine, and you'd be setting yourself back way too much if you didn't.

Should I try to keep my level of math at least a class higher than the physics class that requires it?

In some ways this is ideal, but not if it ruins your degree schedule. Even aside from this, I don't know that it's categorically better to do the math first. Sometimes the physics gives more intuition, is necessary to motivate the math, etc.

That said, I would still study as much integral calculus as you can during the summer.

Pretty much the same:

https://en.wikipedia.org/wiki/Root_test