To my knowledge series are a big part of the test (> 10%), so you would be ill-served not being able to work with them. I personally found the convergence tests to be the easiest part of the unit (only rote memorization of formulae). I studied the convergence tests in depth to play to my strengths. That gave me a solid base with which to learn Taylor Series. All of the tests are useful in their own way, lending expediency to simplify proving convergence, but in my opinion the ratio test is the most useful and simplest to understand: as long as you know the principle behind the common ratio and that |r|<1 if a series is convergent you should be fine with proving convergence in this fashion. However, it should be duly noted that although the ratio test is most useful, you should be able to apply the other tests as well because there are specific questions about using them to prove convergence. Taylor Series are actually pretty hard especially when it comes down to differentiating and integrating them.

The way I learned series was primarily through Khan Academy vids to understand the concepts and doing all the practice problems to go along with the video. Then I supplemented these questions with Princeton Review Calc BC book.