Spivak has a pretty decent calculus textbook that you might find interesting. I used a different textbook, but I believe that Spivak is more popular.
Doing epsilon–delta proofs can be fun, but it’s mostly useful for aspiring pure mathematicians, and not really relevant per se for the grandparent poster.
> [I] am now in a graduate CS program, I feel like I’m missing the deeper understanding of many of the formulas that are presented
> My plan is to get through it to get some background on the main ideas of calculus
Doing delta–epsilon proofs isn’t necessary to clear that up though. Just a regular introductory calculus curriculum is likely sufficient.