I could use some help navigating which areas of Computational Complexity (e.g. CCC, STOC topics) require the least amount of background knowledge to get involved in basic research. I am looking to focus on such topics to get momentum in thinking about Computational Complexity research problems. Are there exercises in particular texts that are good warm up or moderately hard problems in those topics to get started?
I have studied most topics in CS, the basics of applied math/calculus, introductory combinatorics, and introductory information theory. I have not studied linear algebra, abstract algebra, probability. I am happy to learn more about each topic gradually, but I am looking for some initial area in complexity that requires few of those topics, to get a foothold in understanding some topic deeply.