The job of laying out a course of study in algorithms - and the other things you need to know to put them to use - especially one that leads to a career in computers, is the job of laying out the syllabus of a university course in Computer Science. Indeed I suspect that some universities provide little value except to lay out the syllabus and assess the students - the students do pretty much everything else for themselves. If at all possible, your goal should be to prepare yourself to get onto a course in Computer Science, whether by full or part time study.
My book recommendation would be "The Practice Of Programming," by Kernighan and Pike, especially if you plan to learn by doing. It doesn't go very deeply into algorithms, but in a few pages it should tell you enough about design and testing that when you practice you will find, fix, and learn from many of your mistakes, and get into the habit of writing programs that other people can look at without grimacing.
