Textbook recommandation on the topology of fibre bundles (modern)

Question

Here is a little introduction that you might want to skip if you want :

Introduction

I've used math stackexchange to find many (very useful) recommandations of textbooks on various subjects in the past ! Indeed, finding a textbook that suits a student is a critical thing to me. I'm studying in France and in my school the students (which I am part) are often overwhelmed by very formal and huge polycopiés written by our own teachers following the model template :

Definition
Proposition
Corollary
Remark
...

and so on, without any explanation or intuition. I find it very very hard as a first encounter with some subjects (such as differential geometry, algebraic topology , complex analysis ...) and I quickly went to no class at all and used books to work by myself. But in order to make this work, one must find a book that suits its way of thinking math. It strikes me that I might absolutely love a book and find its treatment of the subject limpid while some of my fellows would find it absolutely unreadable. That's how I understood the importance of finding YOUR book in the subject. Luckily, on math stackexchange, there are already many threads concerning recommandation of math textbooks and what I love is that in these threads, one always ends up with a long list of books with reviews that explain how the subject is treated which allows one to make up his mind on his affinity with each book. It goes without saying that I probably already found 4-5 wonderful textbooks this way and I must greatly thank people that wrote all these reviews.

I started with undergraduate subjects which usually have plenty of textbooks that can suit almost anyone but with time passing, I am now studying graduate subjects and I find it sometimes harder to find a good reference because, of course, there are less of it so there is a weaker chance to find one suiting you more or less. I have tried to find all the recommandation threads on what is interesting me but I haven't found a book suiting me well so I thought I'd rather ask for recommandations directly !

The question

I want to study the topology of fiber bundles. More precisely, I'm following a course named "Algebraic topology of manifolds" (in french, the language of the course it's "Topologie algébrique des variétés) which contains more or less

1. Vector bundles (definition and few properties)
2. Classification of Vector bundles and homotopy
3. Characteristic classes
4. Poincaré duality

And also fondamental classes, De Rham cohomology.It's kind of a mixup but for what I've read of the course it looks to me that it's about topology of fiber bundles.

I found online and by looking at a few books on fiber bundles that they are mainly geometrical (Husemoller's for instance) but as I want to do homological algebra and symplectic topology later, I'm looking for a more algebraic treatment but still with the geometric intuition behind if it's possible. Of course, I lack knowledge on the subject of fiber bundles so I might have a wrong intuition of the books or even of the subject so please feel free to correct me or whatever :) ! I've also looked at "The topology of fibre bundles" by Steenrod but I found it very formal and very dense and not really readable. I have Hatcher's book at home and I've read that it treats some of the points I've listed above so I'll take a look later to see if I can use it.

Thanks for reading and have a nice day,

Hugo :)