I'm going to answer a little differently in case this would be your first exposure to calculus and since you are self learning. My view is that a lot of rigour is counter productive for a first exposure and it's more important to develop an intuition for what it means and how it might be used. I would recommend a textbook that is heavy on applications, graphs, visuals, intuition and for which solutions are available. These are things that you would normally get from the course instructor as you go but for a self studier they must also be in the textbook.
I will second Smodak's recommendation of
Savov for this purpose. The name of the book really turned me off at first but when I started reading it, I found it to be really good and chock full of the kinds of things a prof or a tutor might tell you ("don't forget that this relates to this other thing" or "people often mistake this for this other thing, here's why they're not the same", etc.).
The other option I suggest as a more traditional first exposure to Calculus is
https://www.amazon.com/dp/1285741552/?tag=pfamazon01-20 This one is used in many universities for their introduction to calculus, and as a result is extremely polished, tries to appeal to a wide audience but is expensive. It has lots of great colourful graphs, visualizations, solution manuals available and provides examples of applications to many different fields. (You can save a lot of money by getting a used, older version. The main difference between them is that the exercises get revised every few years to help profs save time on finding problems whose solutions can't be easily found using google.)
Once you have the idea of calculus in your head, you may enjoy moving on to something rigorous like Spivak's Calculus text, which is widely praised and loved among people who have already had some basic exposure to Calculus. Going through Spivak would take you more in the direction of how a mathematician views calculus rather than as physicists and engineers tend to see it, which is as a tool.
The other recommendations for books on differential equations are another good step afterwards. If you've not heard of diff equations before, here's an analogy: in the same way that grade school students first learn how to multiply two expressions, then how to do the inverse, dividing them, and later they learn how to solve equations that incorporate the need to multiply and divide... here it's the same thing. In calculus, you learn how to differentiate expressions and then how to do the inverse, integrate expressions, then in "differential equations" you learn how to solve equations that incorporate the need to differentiate and integrate.
