I'd like to leave a comment instead of an answer, since my "answer" wont be definite. However, i'm quite new so i don't have the reputation to leave a comment. But i think i have something useful to say, so i'll take this opportunity.
To start, could you be more specific on what you already know about? What do you know about differential and complex geometry? How is your knowledge of commutative algebra? Are you an undergraduate or grad student?
And are you a mathematician or do you study something else and need to learn algebraic geometry?
If i'm honest, i must admit i am a little confused by your dislike of the theorem-proof structure, since it is quite standard.
Now the books.
A professor at my uni recommended Miles Reid - Undergraduate Algebraic Geometry. As the title gives away, its written for undergraduates. As i was already a grad student when i got it, i didn't read much of it. However, i can say that there is an excellent introduction focusing both on the history and motivation that you mentioned (it helped me even when i already learned a big part of Hartshorne). Also the down-to-earth approach helped me in some cases where books like Hartshorne were too abstract to grasp. The treatment of the tangent space of a variety is excellent, for example.
When i was learning about schemes, a classmate of mine was enthousiastic about the notes of Andreas Gathmann. They are supposed to contain motivation and examples, but i have rarely used them myself so this is not my personal experience.
As i mentioned, i have no idea about your level, but i just took a quick look and Gathmann starts at the basis i believe (varieties, Zariski topology...)
I could also recommend Ravi Vakil's notes. I haven't used them a lot but they tend to show up everywhere and i guess that's for a reason. I found the style very accesible.
Lastly, please reconsider Hartshorne, but you should use it in the right way. The style of writing is really compact, so if you read it, get used to using a lot of other resources. For example, when i learned about "injective objects in a category", it took my professor a substantial part of the lecture, however Hartshorne spends a few sentences about the definition.
So when reading Hartshorne, don't: expect a lot of intuition and background.
Do: consider it your atlas, your guidance. Use google a lot (loads of teachers put their lectures online), be prepared to look for background and spend a lot of time on just a few sentences. But everything's there, it's incredibly complete. Spend a LOT of time on the exercises, the book is written for the active learner and a substantial part of the theory is contained in the exercises.
Once you use it in the right way, you'll fall in love. The book is beautiful.
By the way, this guy put a very complete collection of solutions to the exercises online, check it out at
Lastly, if you're interested in surfaces, Beauville: algebraic surfaces is an excellent treatment that contains a lot of historical notes. However, it is a little specialized so i doubt that it is what you're looking for.
Whenever i did not state a reference, just google.
I hope this helps.