One of the classic references to studying algebraic topology is Hatcher's Algebraic Topology, which is available online at Hatcher's webpage. He says the following on the topic of prerequisites:
In terms of prerequisites, the present book assumes the reader has some familiarity with the content of the standard undergraduate courses in algebra and point-set topology. In particular, the reader should know about quotient spaces, or identification spaces as they are sometimes called, which are quite important for algebraic topology.
You should probably study the following collection of topics: topological spaces, continuous maps, connectedness, compactness, separation, function spaces, metrization, embedding theorems, and the fundamental group. You should also know what is taught in a "standard undergraduate course in algebra". A nice collection of notes written by Professor Richard Elman is here.
Since you say that you want to study algebraic topology with a "homotopical viewpoint", you should check out this MathOverflow question. Note: you can actually study homotopy theory through combinatorial objects called simplicial sets, but it's probably better to learn homotopy theory the classic way.
Hope this helps.