Based on people who have maybe used both books, would Tom Apostol's Volume I book be a more preferred book than Stewarts? I'm really aiming to understand everything and not just "know how to do the steps." This is why someone recommended Apostol to me. I am a beginner in Calculus as well, which was a reason why he warned me against Apostol's book as well. I have access to both books at my library so whichever one is the better I will get. If there are any other books, can you recommend them to me as well?
Once you get your feet wet and know "how"to do some calculus, try reading "A Tour of the Calculus" by D Berlinski to get an idea of what's going on in the background, what the underlying assumptions are and what makes the whole thing work. This is an informative (if offbeat) book, and it is certainly not a formal book of proofs, but it may help you understand why some of the proofs in the "real" math books are important. It helped me, anyway. I was always kind of lost in the details during math class, this book is about the big picture.
apostol (or spivak) is appropriate for people who may want to get a phd, while stewart is appropriate for people who just want a cook book acquaintance with the computations of calculus.
My calculus course uses Thomas Calc. for a textbook which i believe is very similar to Stewart, and i do use that, but i also have a copy of Apostol as a second text, and im really happy with it. I do like them both, but i definitly feel that i have a fuller understanding after reading Apostol.