If you want book recommendations, I can recommend Dover Publications books highly. They are inexpensive and often are more easily understood than books from academic publishers. The Dover book Intoduction to Projective Geometry by C. R. Wylie, Jr. seems to be the kind of book you are looking for. As for prerequisites, a feeling for geometry is probably all that you need for a start. Don't expect to understand everything the first time through, unlike a novel. You have to play with the ideas and objects yourself and construct your own understanding. It will grow on you.
There are several approaches to projective geometry. In the metric/analytic approach, the use of cross-ratio is very important. In the combinatorial/incidence approach, the dual incidence relations between lines and points is important including finite projective planes. In the linear algebra approach, the use of homogeneous coordinates in connection with affine and projective spaces is important. In the abstract algebra approach, the algebraic structures that some projective planes support are important. For example, ternary operations or binary operations that may not be commutative or associative. There are probably other approaches and subfields you may encounter.
If you already know some Euclidean geometry, it will give you a wider perspective. For example, all conic sections are projectively equivalent, except for degenerate cases like two intersecting lines. The existence of a "line at infinity" where parallel lines intersect removes exceptions because in projective planes, all line pairs intersect each other. You may also be interested in the unified projective generation of conics. You may find Poncelet's Porism of great interest because it is a purely projective result discovered by the geometer who essentially founded the subject.