Why not look at the course syllabus for bioinformatics training programs? Here's the course list for the program in Vancouver. I'm sure if you search for the other training programs listed in the post you link to they will also have some course lists.
I would say that you first start learning how to program in python, after that (or simultaneously what you priortize is very dependent on your interests. Bioinformatics is an incredibly large field, so think about what you find more intereseting (most of the list overlap somewhat): Transcriptomics, genomics, protein structures, medicine development, epigenomics, if you want to develop tools or want to use them, etc.[?]
It really depends on your interests.
For "generic" bioinformatics, basic programming in a scripting language like Python/Perl and molecular biology courses. Oh, and moving around in a Linux console. These should enable you to then move up to whatever level you need, in whichever field you choose. All you need then is patience and motivation!
The ISCB Education Committee has made a survey to define a "Consensus Bioinformatics Curriculum", the results are here. This includes a question: "What are the most important topics that someone should understand in order to work successfully in the field of computational biology / bioinformatics?" and the results are in Fig. 4 of the Word document.
That will give you an impression, at least, which fields people might find important for bioinformatics education in general.